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Theses

Opérateurs et semi-groupes d’opérateurs sur des espaces de fonctions holomorphes : Applications à la théorie de l’universalité

Abstract : The works in this thesis address topics from operator theory and involves ideas and notions arising from complex analysis, the theory of operator semigroups and the theory of universality. The first main result of this thesis relates to the study of composition operators on spaces of holomorphic functions: we compute the spectrum of an operator of composition by a Koenigs's symbol acting on the space of holomorphic functions on the open unit disk, and derive from it the general description of the spectrum of composition operators on Banach spaces of holomorphic functions. The key tool we develop in this study is a description of spectral projections associated with such operators.The second main result of this thesis relates to the thoery of universality: we extend to operator semigroups the notion of universality. Then, we prove the existence of a universal semigroup for quasi-contractive operators semigroups. We then show a similar result for concave semigroups
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https://tel.archives-ouvertes.fr/tel-02395367
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Submitted on : Thursday, December 5, 2019 - 2:25:07 PM
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TH2019CELARIESBENJAMIN.pdf
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  • HAL Id : tel-02395367, version 1

Citation

Benjamin Célariès. Opérateurs et semi-groupes d’opérateurs sur des espaces de fonctions holomorphes : Applications à la théorie de l’universalité. Variables complexes [math.CV]. Université de Lyon, 2019. Français. ⟨NNT : 2019LYSE1077⟩. ⟨tel-02395367⟩

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