My study triangulates three recurrent Hardyan concerns – gender, interiority, and form – as they are shaped by the sub-genres of the serial novel, the sentimental novel, and the novel of sensation. I explore Thomas Hardy’s adjustments of traditional forms to new paths, including his vision of a new sort of stealth-realism, in the representation of subjectivity. When we consider Hardy’s vexed depictions of gender through the lens of form, the debate over Hardy’s “unfair” (misogynist) or “progressive” (feminist) representations becomes less polarized and allows for broader examinations of Hardy’s experimental impulses. It is my contention that Hardy is relentlessly engaged with female representation – and narrative representation, overall – as a major formal and ideological problem, and that he demonstrably engages with this problem at various levels of remove: his renderings of subjectivity are not simply attempts at faithful depiction, but meta-commentary on the processes of narrative technique and gendered representation.

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<p> The principal object of this study is to find weak and strong type estimates concerning functions in weighted Lp spaces and their maximal functions. We also apply these results to the study of convolution integrals. </p> / Thesis / Master of Science (MSc)

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The Angel in the House: An Unstable Icon examines the ways in which the figure named in Coventry Patmore's series of mid-nineteenth century poems provoked an anxiety that manifests itself consistently in British literature throughout the nineteenth and into the twentieth century, where the family beacon, the one whose raison d'être was to guide her husband and children away from the immorality rife in the public sphere, instead actively interfered with the good instincts of her offspring, substituted her own wishes for theirs, and caused irreparable harm in the process. This dissertation analyzes the ways in which mother figures in mid-century novels interrogate the angel-mother in particular and suggest the destructive capability inherent in that figure. It argues that the literary questioning of the ideal supports what Poovey calls "uneven development" in the construction of a gender model. The Angel in the House: An Unstable Icon will demonstrate that at the hands of Thomas Hardy and Henry James in particular, the mother is reimagined into a figure bearing little resemblance to the Angel mother, except in her inheritance of a belief that the mother must remain her child's guide, despite the inclinations of their adult children toward a new autonomy. While the Victorian consciousness seems to have experienced a splitting--women were either good or bad, mothers were either good or bad--Hardy and James resist such splitting, instead exploring the gaps and flaws in the Angel-in-the-House ideology, in the process establishing the prototype for mother figures who little resemble Angels, in other words, fully human mothers, that both British and American Modernists such as D. H. Lawrence, William Faulkner, and Virginia Woolf would adapt as central figures in their major works. / English

Titre de l'écran-titre (visionné le 13 novembre 2023) / Dans les dernières années, un analogue non linéaire aux séries de Fourier a intéressé plusieurs mathématiciens. Ce dernier permet d'approximer un signal par une somme de termes dont les composantes représentent la fréquence et l'amplitude. Il s'agit du déroulement de Blaschke de fonctions analytiques introduit par Coifman, ou développement de Fourier adaptatif. L'idée de Coifman a été de factoriser toutes les racines dans le disque unité en interprétant les monômes z ↦ zⁿ présents dans la série de Taylor comme des produits de Blaschke. Il a aussi utilisé la factorisation de Blaschke pour les fonctions analytiques sur un voisinage du disque unité. Ce développement en série a été appliqué à plusieurs autres problèmes depuis, car il présente de nombreux avantages sur les séries de Fourier classiques. Néanmoins, la question de convergence de cette représentation en série est un problème majeur depuis plusieurs décennies. On sait seulement qu'il y a convergence de la série dans certains sous-espaces de H² avec poids et, par des résultats récents, dans les espaces de Hardy. Dans ce mémoire, on présente un déroulement de fonctions dans les espaces de Hilbert à noyau reproduisant et dans les espaces de Hardy qui est une généralisation du déroulement de Blaschke et qui est inspiré par la théorie des opérateurs et les espaces de de Branges-Rovnyak. Pour ce faire, on développe d'abord les notions préalables de l'analyse complexe, harmonique et fonctionnelle. Nos résultats principaux sont des théorèmes de convergence pour ces développements en série. Quelques applications et exemples sont aussi présentés. / Over the last few years, many mathematicians became interested in a nonlinear analogue of Fourier series that allows them to approximate a signal by a sum of terms whose components represent frequency and amplitude. It is the Blaschke unwinding series introduced by Coifman, or adaptive Fourier decomposition. Coifman's idea was to factor all the roots in the unit disk by thinking of the monomials z ↦ zⁿ in the Taylor series as Blaschke products. He also used the Blaschke factorization for analytic functions in a neighbourhood of the unit disk. Because it has many advantages over the classical Fourier series, this series expansion has been used in several other problems since. Yet, the question of convergence of the series has remained a major problem for a few decades. We only know that it converges in certain weighted subspaces of H² and, by recent work, in Hardy spaces. In this thesis, we introduce an expansion scheme in reproducing kernel Hilbert spaces and Hardy spaces. It is a generalization of the Blaschke unwinding series expansion which is motivated by operator theory and de Branges-Rovnyak spaces. To do this, we first introduce the necessary background material in complex analysis, harmonic analysis, and functional analysis. Our main results are convergence theorems for these series expansions. We also present some applications and examples.

Hardy space scalar theory on the disk is now classical. Some extensions have been done, one of them is the approach done by Donald Sarason using Laurent series. We present the more complicated function theory, without the use of either power series or Laurent series, for finitely-connected planar domains. / Master of Science