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Die Abteilung Kunstschutz der deutschen Wehrmacht im besetzten Griechenland (1941-1944) bestand aus wehrpflichtigen deutschen Archäologen. Sie waren zunächst Stipendiaten oder Mitarbeiter des Archäologischen Instituts des Deutschen Reiches (AIDR) unter den Bedingungen des Nationalsozialismus, bevor sie im Zweiten Weltkrieg in der Uniform der Wehrmacht zurückkehrten. Ihre Biografien im Kontext der Abteilung Athen, deren Direktor Georg Karo bis 1936 war, sowie der Zentrale der Instituts, unter dem von 1932 bis 1936 amtierenden Präsidenten Theodor Wiegand, sind ein Untersuchungsgegenstand. Die außenpolitische Legitimation des NS-Regimes durch die Olympischen Spiele und der wichtigste wissenschaftspolitische Erfolg des Institutes, die Wiederaufnahme der Olympiagrabung, die Wiegand und Karo seit 1933 anstrebten und durch ihre politischen Netzwerke 1936 erreichten, werden in der Dissertation in ihrer wechselseitigen Bedingtheit aufgezeigt. Diese Anpassungsleistungen an das NS-Regime prägten den eigenen archäologischen Nachwuchs aber auch die griechische Gesellschaft.
Schutzmaßnahmen waren nur ein kleiner Tätigkeitsbereich der Kunstschützer aber ein wichtiger Teil der Wehrmachtspropaganda. Der Institutspräsident Martin Schede (1937 bis 1945) forderte Mitarbeitern vor allem für zwei AIDR-Projekte an: die Erstellung von Flugbildern von möglichst ganz Griechenland und Ausgrabungen auf Kreta. Bereits diese Zwischenergebnisse berechtigen zu dem Titel „Kunstschutz als Alibi“.
Die Dissertation versucht, die Frage zu beantworten, warum der archäologische Kunstschutz nicht mehr als ein Alibi sein konnte. Dies geschieht vor allem unter Berücksichtigung der politischen aber auch der militärischen Traditionslinien deutscher Archäologie in Griechenland und Deutschland.
Case-Based Reasoning (CBR) is a symbolic Artificial Intelligence (AI) approach that has been successfully applied across various domains, including medical diagnosis, product configuration, and customer support, to solve problems based on experiential knowledge and analogy. A key aspect of CBR is its problem-solving procedure, where new solutions are created by referencing similar experiences, which makes CBR explainable and effective even with small amounts of data. However, one of the most significant challenges in CBR lies in defining and computing meaningful similarities between new and past problems, which heavily relies on domain-specific knowledge. This knowledge, typically only available through human experts, must be manually acquired, leading to what is commonly known as the knowledge-acquisition bottleneck.
One way to mitigate the knowledge-acquisition bottleneck is through a hybrid approach that combines the symbolic reasoning strengths of CBR with the learning capabilities of Deep Learning (DL), a sub-symbolic AI method. DL, which utilizes deep neural networks, has gained immense popularity due to its ability to automatically learn from raw data to solve complex AI problems such as object detection, question answering, and machine translation. While DL minimizes manual knowledge acquisition by automatically training models from data, it comes with its own limitations, such as requiring large datasets, and being difficult to explain, often functioning as a "black box". By bringing together the symbolic nature of CBR and the data-driven learning abilities of DL, a neuro-symbolic, hybrid AI approach can potentially overcome the limitations of both methods, resulting in systems that are both explainable and capable of learning from data.
The focus of this thesis is on integrating DL into the core task of similarity assessment within CBR, specifically in the domain of process management. Processes are fundamental to numerous industries and sectors, with process management techniques, particularly Business Process Management (BPM), being widely applied to optimize organizational workflows. Process-Oriented Case-Based Reasoning (POCBR) extends traditional CBR to handle procedural data, enabling applications such as adaptive manufacturing, where past processes are analyzed to find alternative solutions when problems arise. However, applying CBR to process management introduces additional complexity, as procedural cases are typically represented as semantically annotated graphs, increasing the knowledge-acquisition effort for both case modeling and similarity assessment.
The key contributions of this thesis are as follows: It presents a method for preparing procedural cases, represented as semantic graphs, to be used as input for neural networks. Handling such complex, structured data represents a significant challenge, particularly given the scarcity of available process data in most organizations. To overcome the issue of data scarcity, the thesis proposes data augmentation techniques to artificially expand the process datasets, enabling more effective training of DL models. Moreover, it explores several deep learning architectures and training setups for learning similarity measures between procedural cases in POCBR applications. This includes the use of experience-based Hyperparameter Optimization (HPO) methods to fine-tune the deep learning models.
Additionally, the thesis addresses the computational challenges posed by graph-based similarity assessments in CBR. The traditional method of determining similarity through subgraph isomorphism checks, which compare nodes and edges across graphs, is computationally expensive. To alleviate this issue, the hybrid approach seeks to use DL models to approximate these similarity calculations more efficiently, thus reducing the computational complexity involved in graph matching.
The experimental evaluations of the corresponding contributions provide consistent results that indicate the benefits of using DL-based similarity measures and case retrieval methods in POCBR applications. The comparison with existing methods, e.g., based on subgraph isomorphism, shows several advantages but also some disadvantages of the compared methods. In summary, the methods and contributions outlined in this work enable more efficient and robust applications of hybrid CBR and DL in process management applications.
There is a wide range of methodologies for policy evaluation and socio-economic impact assessment. A fundamental distinction can be made between micro and macro approaches. In contrast to micro models, which focus on the micro-unit, macro models are used to analyze aggregate variables. The ability of microsimulation models to capture interactions occurring at the micro-level makes them particularly suitable for modeling complex real-world phenomena. The inclusion of a behavioral component into microsimulation models provides a framework for assessing the behavioral effects of policy changes.
The labor market is a primary area of interest for both economists and policy makers. The projection of labor-related variables is particularly important for assessing economic and social development needs, as it provides insight into the potential trajectory of these variables and can be used to design effective policy responses. As a result, the analysis of labor market behavior is a primary area of application for behavioral microsimulation models. Behavioral microsimulation models allow for the study of second-round effects, including changes in hours worked and participation rates resulting from policy reforms. It is important to note, however, that most microsimulation models do not consider the demand side of the labor market.
The combination of micro and macro models offers a possible solution as it constitutes a promising way to integrate the strengths of both models. Of particular relevance is the combination of microsimulation models with general equilibrium models, especially computable general equilibrium (CGE) models. CGE models are classified as structural macroeconomic models, which are defined by their basis in economic theory. Another important category of macroeconomic models are time series models. This thesis examines the potential for linking micro and macro models. The different types of microsimulation models are presented, with special emphasis on discrete-time dynamic microsimulation models. The concept of behavioral microsimulation is introduced to demonstrate the integration of a behavioral element into microsimulation models. For this reason, the concept of utility is introduced and the random utility approach is described in detail. In addition, a brief overview of macro models is given with a focus on general equilibrium models and time series models. Various approaches for linking micro and macro models, which can either be categorized as sequential approaches or integrated approaches, are presented. Furthermore, the concept of link variables is introduced, which play a central role in combining both models. The focus is on the most complex sequential approach, i.e., the bi-directional linking of behavioral microsimulation models with general equilibrium macro models.
The goal of this work is to compare operators that are defined on probably varying Hilbert spaces. Distance concepts for operators as well as convergence concepts for such operators are explained and examined. For distance concepts we present three main notions. All have in common that they use space-linking operators that connect the spaces. At first, we look at unitary maps and compare the unitary orbits of the operators. Then, we consider isometric embeddings, which is based on a concept of Joachim Weidmann. Then we look at contractions but with more norm equations in comparison. The latter idea is based on a concept of Olaf Post called quasi-unitary equivalence. Our main result is that the unitary and isometric distances are equal provided the operators are both self-adjoint and have 0 in their essential spectra. In the third chapter, we focus specifically on the investigation of these distance terms for compact operators or operators in p-Schatten classes. In this case, the interpretation of the spectra as null sequences allows further distance investigation. Chapter four deals mainly with convergence terms of operators on varying Hilbert spaces. The analyses in this work deal exclusively with concepts of norm resolvent convergence. The main conclusion of the chapter is that the generalisation for norm resolvent convergence of Joachim Weidmann and the generalisation of Olaf Post, called quasi-unitary equivalence, are equivalent to each other. In addition, we specify error bounds and deal with the convergence speed of both concepts. Two important implications of these convergence notions are that the approximation is spectrally exact, i.e., the spectra converge suitably, and that the convergence is transferred to the functional calculus of the bounded functions vanishing at infinity.
In this dissertation, I analyze how large players in financial markets exert influence on smaller players and how this affects the decisions of the large ones. I focus on how the large players process information in an uncertain environment, form expectations and communicate these to smaller players through their actions. I examine these relationships empirically in the foreign exchange market and in the context of a game-theoretic model of an investment project.
In Chapter 2, I investigate the relationship between the foreign exchange trading activity of large US-based market participants and the volatility of the nominal spot exchange rate. Using a novel dataset, I utilize the weekly growth rate of aggregate foreign currency positions of major market participants to proxy trading activity in the foreign exchange market. By estimating the heterogeneous autoregressive model of realized volatility (HAR-RV), I find evidence of a positive relationship between trading activity and volatility, which is mainly driven by unexpected changes in trading activity and is asymmetric for some of the currencies considered. My results contribute to the understanding of the drivers of exchange rate volatility and the role of large players in the flow of information in financial markets.
In Chapters 3 and 4, I consider a sequential global game of an investment project to examine how a large creditor influences the decisions of small creditors with her lending decision. I pay particular attention to the timing of the large player’s decision, i.e. whether she makes her decision to roll over a credit before or after the small players. I show that she faces a trade-off between signaling to and learning from small creditors. By being a focal point for coordination, her actions have a substantial impact on the probability of coordination failure and the failure of the investment project. I investigate the sensitivity of the equilibrium by comparing settings with perfect and imperfect learning. The results highlight the importance of signaling and provide a new perspective on the idea of catalytic finance and the influence of a lender-of-last-resort in self-fulfilling debt crises.
Globalization significantly transforms labor markets. Advances in production technologies, transportation, and political integration reshape how and where goods and services are produced. Local economic conditions and diverse policy responses create varying speeds of change, affecting regions' attractiveness for living and working -- and promoting mobility.
Competition for talent necessitates a deep understanding of why individuals choose specific destinations, how to ensure their effective labor market integration, and what workplace factors affect workers' well-being.
This thesis focuses on two crucial aspects of labor market change -- Migration and workplace technological change. It contributes to our understanding of the determinants of labor mobility, the factors facilitating migrant integration, and the role of workplace automation for worker well-being.
Chapter 2 investigates the relationship between minimum wages (MWs) and regional worker mobility in the EU. EU citizens are free to work anywhere in the common market, which allows them to take advantage of the significant variation in MWs across the EU. However, although MWs are set at the national level, it is also their local relevance that varies substantially -- depending on factors such as the share of affected workers or the extent to which they shift local compensation levels. These variations may attract workers from elsewhere, from within a country or from abroad.
Analyzing regional variations in the Kaitz index, a measure of local MW impact, reveals that higher MWs can significantly increase inflows of low-skilled EU workers, particularly in central Europe.
Chapter 3 examines the inequality in returns to skills experienced by immigrants, focusing on the role of linguistic proximity between migrants' origin and destination countries. Harmonized individual-level data from nine linguistically diverse migrant-hosting economies allows for an analysis of the wage gaps faced by immigrants from various origins, implicitly indicating how well they and their skills are integrated into the local labor markets. The analysis reveals that greater linguistic distance is associated with a higher wage penalty for highly skilled immigrants and a lower position in the wage distribution for those without tertiary education.
Chapter 4 investigates an institutional factor potentially relevant for the integration of immigrants -- the labor market impact of Confucius Institutes (CIs), Chinese government-sponsored institutions that promote Chinese language and culture abroad. CIs have been found to foster trade and cultural exchange, indicating their potential relevance in shaping attitudes and trust of natives towards China and Chinese individuals. Examining the relationship between local CI presence and the wages of Chinese immigrants in local labor markets of the United States, the analysis reveals that CIs associate with significantly reduced wages for nearby residing Chinese immigrants. An event study demonstrates that the mere announcement of a new CI negatively impacts local wages for Chinese immigrants, independent of the CI's actual opening.
Chapter 5 explores how working in automatable jobs affects life satisfaction in Germany. Following earlier literature, we classify occupations by potential for automation, and define the top third of occupations in this metric as \textit{automatable jobs}. We find workers in highly automatable jobs reporting a lower life satisfaction. Moreover, we detect a non-linearity, where workers in moderately automatable jobs (the second third of the distribution) experience a positive association with life satisfaction. Overall, the negative relationship of automation is most pronounced among younger and blue-collar workers, irrespective of the non-linearity.
Ensuring fairness in machine learning models is crucial for ethical and unbiased automated decision-making. Classifications from fair machine learning models should not discriminate against sensitive variables such as sexual orientation and ethnicity. However, achieving fairness is complicated by biases inherent in training
data, particularly when data is collected through group sampling, like stratified or
cluster sampling as often occurs in social surveys. Unlike the standard assumption of
independent observations in machine learning, clustered data introduces correlations that can amplify biases, especially when cluster assignment is linked to the target variable.
To address these challenges, this cumulative thesis focuses on developing methods to mitigate unfairness in machine learning models. We propose a fair mixed effects support vector machine algorithm, a Cluster-Regularized Logistic Regression and a fair Generalized Linear Mixed Model based on boosting, all of them
are capable of handling both grouped data and fairness constraints simultaneously. Additionally, we introduce a Julia package, FairML.jl, which provides a comprehensive framework for addressing fairness issues. This package offers a preprocessing technique, based on resampling methods, to mitigate biases in the data, as well as a post-processing method, that seeks for a optimal cut-off selection.
To improve fairness in classifications both processes can be incorporated in any
classification method available in the MLJ.jl package. Furthermore, FairML.jl incorporates in-processing approaches, such as optimization-based techniques for logistic regression and support vector machine, to directly address fairness during
model training in regular and mixed models.
By accounting for data complexities and implementing various fairness-enhancing
strategies, our work aims to contribute to the development of more equitable and reliable machine learning models.
This dissertation addresses the measurement and evaluation of the energy and resource efficiency of software systems. Studies show that the environmental impact of Information and Communications Technologies (ICT) is steadily increasing and is already estimated to be responsible for 3 % of the total greenhouse gas (GHG) emissions. Although it is the hardware that consumes natural resources and energy through its production, use, and disposal, software controls the hardware and therefore has a considerable influence on the used capacities. Accordingly, it should also be attributed a share of the environmental impact. To address this softwareinduced impact, the focus is on the continued development of a measurement and assessment model for energy and resource-efficient software. Furthermore, measurement and assessment methods from international research and practitioner communities were compared in order to develop a generic reference model for software resource and energy measurements. The next step was to derive a methodology and to define and operationalize criteria for evaluating and improving the environmental impact of software products. In addition, a key objective is to transfer the developed methodology and models to software systems that cause high consumption or offer optimization potential through economies of scale. These include, e. g., Cyber-Physical Systems (CPS) and mobile apps, as well as applications with high demands on computing power or data volumes, such as distributed systems and especially Artificial Intelligence (AI) systems.
In particular, factors influencing the consumption of software along its life cycle are considered. These factors include the location (cloud, edge, embedded) where the computing and storage services are provided, the role of the stakeholders, application scenarios, the configuration of the systems, the used data, its representation and transmission, or the design of the software architecture. Based on existing literature and previous experiments, distinct use cases were selected that address these factors. Comparative use cases include the implementation of a scenario in different programming languages, using varying algorithms, libraries, data structures, protocols, model topologies, hardware and software setups, etc. From the selection, experimental scenarios were devised for the use cases to compare the methods to be analyzed. During their execution, the energy and resource consumption was measured, and the results were assessed. Subtracting baseline measurements of the hardware setup without the software running from the scenario measurements makes the software-induced consumption measurable and thus transparent. Comparing the scenario measurements with each other allows the identification of the more energyefficient setup for the use case and, in turn, the improvement/optimization of the system as a whole. The calculated metrics were then also structured as indicators in a criteria catalog. These indicators represent empirically determinable variables that provide information about a matter that cannot be measured directly, such as the environmental impact of the software. Together with verification criteria that must be complied with and confirmed by the producers of the software, this creates a model with which the comparability of software systems can be established.
The gained knowledge from the experiments and assessments can then be used to forecast and optimize the energy and resource efficiency of software products. This enables developers, but also students, scientists and all other stakeholders involved in the life cycleof software, to continuously monitor and optimize the impact of their software on energy and resource consumption. The developed models, methods, and criteria were evaluated and validated by the scientific community at conferences and workshops. The central outcomes of this thesis, including a measurement reference model and the criteria catalog, were disseminated in academic journals. Furthermore, the transfer to society has been driven forward, e. g., through the publication of two book chapters, the development and presentation of exemplary best practices at developer conferences, collaboration with industry, and the establishment of the eco-label “Blue Angel” for resource and energy-efficient software products. In the long term, the objective is to effect a change in societal attitudes and ultimately to achieve significant resource savings through economies of scale by applying the methods in the development of software in general and AI systems in particular.
The gender wage gap in labor market outcomes has been intensively investigated for decades, yet it remains a relevant and innovative research topic in labor economics. Chapter 2 of this dissertation explores the pressing issue of gender wage disparity in Ethiopia. By applying various empirical methodologies and measures of occupational segregation, this chapter aims to analyze the role of female occupational segregation in explaining the gender wage gap across the pay distribution. The findings reveal a significant difference in monthly wages, with women consistently earning lower wages across the wage distribution.
Importantly, the result indicates a negative association between female occupational segregation and the average earnings of both men and women. Furthermore, the estimation result shows that female occupational segregation partially explains the gender wage gap at the bottom of the wage distribution. I find that the magnitude of the gender wage gap in the private sector is higher than in the public sector.
In Chapter 3, the Ethiopian Demography and Health Survey data are leveraged to explore the causal relationship between female labor force participation and domestic violence. Domestic violence against women is a pervasive public health concern, particularly in Africa, including Ethiopia, where a significant proportion of women endure various forms of domestic violence perpetrated by intimate partners. Economic empowerment of women through increased participation in the labor market can be one of the mechanisms for mitigating the risk of domestic violence.
This study seeks to provide empirical evidence supporting this hypothesis. Using the employment rate of women at the community level as an instrumental variable, the finding suggests that employment significantly reduces the risk of domestic violence against women. More precisely, the result shows that women’s employment status significantly reduces domestic violence by about 15 percentage points. This finding is robust for different dimensions of domestic violence, such as physical, sexual, and emotional violence.
By examining the employment outcomes of immigrants in the labor market, Chapter 4 extends the dissertation's inquiry to the dynamics of immigrant economic integration into the destination country. Drawing on data from the German Socio-Economic Panel, the chapter scrutinizes the employment gap between native-born individuals and two distinct groups of first-generation immigrants: refugees and other migrants. Through rigorous analysis, Chapter 4 aims to identify the factors contributing to disparities in employment outcomes among these groups. In this chapter, I aim to disentangle the heterogeneity characteristic of refugees and other immigrants in the labor market, thereby contributing to a deeper understanding of immigrant labor market integration in Germany.
The results show that refugees and other migrants are less likely to find employment than comparable natives. The refugee-native employment gap is much wider than other migrant-native employment gap. Moreover, the findings vary by gender and migration categories. While other migrant men do not differ from native men in the probability of being employed, refugee women are the most disadvantaged group compared to other migrant women and native women in the probability of being employed. The study suggests that German language proficiency and permanent resident permits partially explain the lower employment probability of refugees in the German labor market.
Chapter 5 (co-authored with Uwe Jirjahn) utilizes the same dataset to explore the immigrant-native trade union membership gap, focusing on the role of integration in the workplace and into society. The integration of immigrants into society and the workplace is vital not only to improve migrant's performance in the labor market but also to actively participate in institutions such as trade unions. In this study, we argue that the incomplete integration of immigrants into the workplace and society implies that immigrants are less likely to be union members than natives. Our findings show that first-generation immigrants are less likely to be trade union members than natives. Notably, the analysis shows that the immigrant-native gap in union membership depends on immigrants’ integration into the workplace and society. The gap is smaller for immigrants working in firms with a works council and having social contacts with Germans. Moreover, the results reveal that the immigrant-native union membership gap is decreasing in the year since arrival in Germany.
Although universality has fascinated over the last decades, there are still numerous open questions in this field that require further investigation. In this work, we will mainly focus on classes of functions whose Fourier series are universal in the sense that they allow us to approximate uniformly any continuous function defined on a suitable subset of the unit circle.
The structure of this thesis is as follows. In the first chapter, we will initially introduce the most important notation which is needed for our following discussion. Subsequently, after recalling the notion of universality in a general context, we will revisit significant results concerning universality of Taylor series. The focus here is particularly on universality with respect to uniform convergence and convergence in measure. By a result of Menshov, we will transition to universality of Fourier series which is the central object of study in this work.
In the second chapter, we recall spaces of holomorphic functions which are characterized by the growth of their coefficients. In this context, we will derive a relationship to functions on the unit circle via an application of the Fourier transform.
In the second part of the chapter, our attention is devoted to the $\mathcal{D}_{\textup{harm}}^p$ spaces which can be viewed as the set of harmonic functions contained in the $W^{1,p}(\D)$ Sobolev spaces. In this context, we will also recall the Bergman projection. Thanks to the intensive study of the latter in relation to Sobolev spaces, we can derive a decomposition of $\mathcal{D}_{\textup{harm}}^p$ spaces which may be seen as analogous to the Riesz projection for $L^p$ spaces. Owing to this result, we are able to provide a link between $\mathcal{D}_{\textup{harm}}^p$ spaces and spaces of holomorphic functions on $\mathbb{C}_\infty \setminus \s$ which turns out to be a crucial step in determining the dual of $\mathcal{D}_{\textup{harm}}^p$ spaces.
The last section of this chapter deals with the Cauchy dual which has a close connection to the Fantappié transform. As an application, we will determine the Cauchy dual of the spaces $D_\alpha$ and $D_{\textup{harm}}^p$, two results that will prove to be very helpful later on. Finally, we will provide a useful criterion that establishes a connection between the density of a set in the direct sum $X \oplus Y$ and the Cauchy dual of the intersection of the respective spaces.
The subsequent chapter will delve into the theory of capacities and, consequently, potential theory which will prove to be essential in formulating our universality results. In addition to introducing further necessary terminologies, we will define capacities in the first section following [16], however in the frame of separable metric spaces, and revisit the most important results about them.
Simultaneously, we make preparations that allow us to define the $\mathrm{Li}_\alpha$-capacity which will turn out to be equivalent to the classical Riesz $\alpha$-capacity. The $\mathrm{Li}_\alpha$-capacity proves to be more adapted to the $D_\alpha$ spaces. It becomes apparent in the course of our discussion that the $\mathrm{Li}_\alpha$-capacity is essential to prove uniqueness results for the class $D_\alpha$. This leads to the centerpiece of this chapter which forms the energy formula for the $\mathrm{Li}_\alpha$-capacity on the unit circle. More precisely, this identity establishes a connection between the energy of a measure and its corresponding Fourier coefficients. We will briefly deal with the complement-equivalence of capacities before we revisit the concept of Bessel and Riesz capacities, this time, however, in a much more general context, where we will mainly rely on [1]. Since we defined capacities on separable metric spaces in the first section, we can draw a connection between Bessel capacities and $\mathrm{Li}_\alpha$-capacities. To conclude this chapter, we would like to take a closer look at the geometric meaning of capacities. Here, we will point out a connection between the Hausdorff dimension and the polarity of a set, and transfer it to the $\mathrm{Li}_\alpha$-capacity. Another aspect will be the comparison of Bessel capacities across different dimensions, in which the theory of Wolff potentials crystallizes as a crucial auxiliary tool.
In the fourth chapter of this thesis, we will turn our focus to the theory of sets of uniqueness, a subject within the broader field of harmonic analysis. This theory has a close relationship with sets of universality, a connection that will be further elucidated in the upcoming chapter.
The initial section of this chapter will be dedicated to the notion of sets of uniqueness that is specifically adapted to our current context. Building on this concept, we will recall some of the fundamental results of this theory.
In the subsequent section, we will primarily rely on techniques from previous chapters to determine the closed sets of uniqueness for the class $\mathcal{D}_{\alpha}$. The proofs we will discuss are largely influenced by [16, p.\ 178] and [9, pp.\ 82].
One more time, it will become evident that the introduction of the $\mathrm{Li}_\alpha$-capacity in the third chapter and the closely associated energy formula on the unit circle, were the pivotal factors that enabled us to carry out these proofs.
In the final chapter of our discourse, we will present our results on universality. To begin, we will recall a version of the universality criterion which traces back to the work of Grosse-Erdmann (see [26]). Coupled with an outcome from the second chapter, we will prove a result that allows us to obtain the universality of a class using the technique of simultaneous approximation. This tool will play a key role in the proof of our universality results which will follow hereafter.
Our attention will first be directed toward the class $D_\alpha$ with $\alpha$ in the interval $(0,1]$. Here, we summarize that universality with respect to uniform convergence occurs on closed and $\alpha$-polar sets $E \subset \s$. Thanks to results of Carleson and further considerations, which particularly rely on the favorable behavior of the $\mathrm{Li}_\alpha$-kernel, we also find that this result is sharp. In particular, it may be seen as a generalization of the universality result for the harmonic Dirichlet space.
Following this, we will investigate the same class, however, this time for $\alpha \in [-1,0)$. In this case, it turns out that universality with respect to uniform convergence occurs on closed and $(-\alpha)$-complement-polar sets $E \subset \s$. In particular, these sets of universality can have positive arc measure. In the final section, we will focus on the class $D_{\textup{harm}}^p$. Here, we manage to prove that universality occurs on closed and $(1,p)$-polar sets $E \subset \s$. Through results of Twomey [68] combined with an observation by Girela and Pélaez [23], as well as the decomposition of $D_{\textup{harm}}^p$, we can deduce that the closed sets of universality with respect to uniform convergence of the class $D_{\textup{harm}}^p$ are characterized by $(1,p)$-polarity. We conclude our work with an application of the latter result to the class $D^p$. We will show that the closed sets of divergence for the class $D^p$ are given by the $(1,p)$-polar sets.