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1	Opérateurs de composition sur les espaces de fonctions holomorphes de plusieurs variables complexes : universalité dans les espaces de Banach et de Fréchet Charpentier, Stéphane 22 November 2010 (has links) Dans la première partie de ma thèse, il est démontré, dans les espaces de Banach et de Fréchet de suites, un résultat d'existence d'un sous-espace fermé de dimension infinie dont les éléments non-nuls sont des séries universelles.La deuxième partie est consacrée à l'étude des opérateurs de composition sur des espaces de fonctions holomorphes de plusieurs variables complexes. Dans un premier temps, le spectre et la dynamique des opérateurs de composition hyperboliques sur les espaces de Hardy de la boule sont décrits complètement.Dans un second temps, la continuité et la compacité des opérateurs de composition sur les espaces de Hardy-Orlicz et de Bergman-Orlicz de la boule sont caractérisées. On en déduit en particulier l'existence d'une classe de fonctions d'Orlicz définissant des espaces du type précédent sur lesquels tout opérateur de composition est continu. / In the first part of my thesis, a result on the existence of a closed infinite-dimensional subspace, whose non-zero elements are universal series, is given in Banach and Fréchet spaces framework.The second part is devoted to the study of composition operators on spaces of several variables analytic functions. First, the spectrum and the dynamics of hyperbolic composition operators acting on Hardy spaces on the ball are completely described.Second, continuity and compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball are characterized. In particular, we deduce from the treatment of the continuity that there exists a class of Orlicz functions which define Hardy-Orlicz and Bergman-Orlicz spaces, on which every composition operator is bounded. Universalité Série universelle Opérateur de composition Espace de Hardy Spectre Hypercyclicité Supercyclicité Cyclicité Homographie Espace de Hardy-Orlicz Espace de Bergman-Orlicz Mesure de Carleson Universality Universal series Composition operator Hardy space Spectrum Hypercyclicity Supercyclicity Cyclicity Homography Hardy-Orlicz space Bergman-Orlicz space Carleson measure
2	Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces Axelsson, Andreas, kax74@yahoo.se January 2002 (has links) The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwells equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator. Dirac operator Maxwell's equations transmission problem Hodge decomposition Cauchy integral double layer potential Lipschitz surface singular integral Carleson measure boundary integral method oblique boundary value problem Fredholm theory exterior algebra Clifford analysis Rellich inequality Banach algebra projection operator Toeplitz operator Calderón projection

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Opérateurs de composition sur les espaces de fonctions holomorphes de plusieurs variables complexes : universalité dans les espaces de Banach et de Fréchet

Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces