Indiana University-Purdue University Indianapolis (IUPUI) / Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as certain restrictions of the unilateral shift on the Hardy space of the disk. A composition operator with symbol fixing 0 has a nested sequence of invariant subspaces, and if the symbol is linear fractional and extremally noncompact, the restrictions to these subspaces all have the same norm and spectrum. Despite this evidence, we will use semigroup techniques to show many cases where the restrictions are still not unitarily equivalent.

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Call number: LD2668 .T4 1938 B41

This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes Ep, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes Hp. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes. The preliminary and background information is given in Chapters 1 and 3 while the main results of this thesis are presented in Chapters 2 and 4. In Chapter 2, I will consider the case of the simply connected domain and the boundary characteristics that allow non-constant analytic functions with real boundary values in certain Smirnov classes. Chapter 4 explores the case of an n-connected domain and the sufficient conditions for which the aforementioned functions exist. In Chapter 5, I will discuss how my results for simply connected domains extend Neuwirth-Newman's Theorem and finish with an open problem for n-connected domains.

This thesis examines the use and representation of letters (and other written messages) in Thomas Hardy's novels, and it considers how Hardy's writing engages with Victorian communication technologies. The 1895 Preface to Far from the Madding Crowd describes Hardy's fictional setting as a ‘a modern Wessex of railways, the penny post, mowing and reaping machines, union workhouses, lucifer matches, labourers who could read and write, and National school children'. The penny post, a communication revolution with an enormous social, economic, and cultural impact, was introduced on 10 January 1840, just a few months before Hardy was born. This thesis aims to demonstrate how a consideration of the material, technological and cultural conditions of communication in Victorian England might reshape our understanding of Hardy's novels, especially of the countless letters, notes, and telegrams which permeate his texts. The written messages in Hardy's novels serve as a means for exploring the process of human communication, and the way this process shapes individual identity, interpersonal relationships, and social interactions alike. Chapter I of this thesis relates Hardy's portrayal of letters to the historical transition from oral tradition to written culture. Chapter II enquires into the relationship between letter writing and notions of privacy and publicity in Hardy's novels. Chapters III and IV argue that Hardy uses letters so as to give a strikingly modern complexity to his representation of human subjectivity and intersubjectivity. The two final chapters investigate how the modalities and technological conditions of written communication influence the construction of Hardy's narratives, the design of his plots. Taken together, the six chapters examine Hardy's perception of one of the most fundamental human activities: communication.

Cette thèse concerne le problème d'identification robuste H indice infini de données harmoniques sur une bande limitée de fréquence, généralisation plus réaliste du problème d'identification robuste H indice infini étudié ces dernières années notamment par Gu, Helmiki, Jacobson, Kargonekhar, Mäkilä, Nett et Partington. L'introduction, en dehors de cette bande, d'un comportement de référence et d'un gabarit rend possible une adaptation des algorithmes classiques en deux étapes, La solution du problème posé est alors donnée par la résolution d'un problème extrémal borné après une première étape d'interpolation robuste des données sur un arc du cercle unité. Cependant, la solution ainsi calculée est typiquement discontinue. La principale contribution de ce travail à l'identification fréquentielle robuste consiste à montrer qu'il est possible de prendre en compte le caractère local des données en fréquence et garantir l'appartenance de la solution à l'algèbre du disque. Un algorithme est donné et sa mise en œuvre numérique est détaillée. Le choix du comportement en dehors de la bande considérée pose plus généralement le problème de complétion analytique borné dans H indice p. Nous le résolvons dans H indice 2 et l'utiliserons pour vérifier la validité de l'hypothèse de linéarité du système.

This thesis compares French educational policy in Morocco and Tunisia during the French protectorate. It concetrates on the evolution of educational systems of both countries before the French colonial era and French reforms of the system. It is based on an analysis of the key figures of the protectorates, the residents-general Cambon and Lyautey and their heads of the education departments Machuel and Hardy. That is achieved through an analysis of their opinions on the educational and colonial policy and their application. The thesis deals with the beginninigs of the protectorate era when the foundations of the French system were laid.

Title: Optimal pairs of function spaces for weighted Hardy operators Author: Rastislav Ol'hava Department: Department of Mathematical Analysis Supervisor of the master thesis: Prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic Abstrakt: We focus on a certain weighted Hardy operator, with a continuous, quasi- concave weight, defined on a rearrangement-invariant Banach function spaces. The op- erators of Hardy type are of great use to the theory of function spaces. The mentioned operator is a more general version of the Hardy operator, whose boundedness was shown to be equivalent to a Sobolev-type embedding inequality. This thesis is con- cerned with the proof of existence of domain and range spaces of our Hardy operator that are optimal. This optimality should lead to the optimality in the Sobolev-type embedding equalities. Our another aim is to study supremum operators, which are also closely related to this issue, and establish some of their basic properties. Keywords: optimality, weighted Hardy operator, supremum operator

This thesis investigates D.H. Lawrence’s idea of the “great background” in the context of Thomas Hardy’s Jude the Obscure and how it reappears in a transformed way in Lawrence’s novels Sons and Lovers, The Rainbow, and Women in Love. Through examining the perverse effects of modernism on these novels’ characters, this thesis argues that the “great background” is something that gradually moves inward––from the old, traditional “State” to an internal, inscrutable yet attainable reality.

The music of Benjamin Britten is both inspiring and intriguing: inspiring, because his music can move the listener; intriguing, because his use of triadic harmonies and rhythmic settings seems at once free, flexible, and spontaneous yet sensible and appropriate in representing the mood of the text. Although many of Britten’s harmonies are traditional in nature, e.g. major and minor triads, it is difficult, almost impossible or cumbersome at best, to assign Roman numerals to his harmonies because his manner of chord progression does not always conform to functional theory. In my analyses, I will demonstrate that the logic behind Britten's harmonic progressions can be explained through two types of neo-Riemannian transformation theories, namely Richard Cohn's Four Hexatonic Systems and Leonhard Euler's Tonnetz. In the case of the "Spinning Scene" from The Rape of Lucretia, Hindemith’s "Table of Chord-Groups" will be used to explain the presence of harmonies that are not part of the four hexatonic systems. Throughout, Schenkerian graphs will be presented to illustrate how the underlying structure and overall harmonic design of each piece work in conjunction with the emotion of the text. In addition, I will show that his rhythmic manipulations, when coupled with the meaning behind his chord progression, vividly paint the emotion of the text, as well as the state of mind of the poet or the character in an opera.