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Versions vectorielles de la description de sous-espaces invariants du shift et de bases de noyaux reproduisants dans certains espaces de fonctions holomorphes.

Abstract : Sarason describes reducing closed subspaces (invarinat by S and $S^{*}$) and doubly invariant (by S and S^{-1}$) of the Hardy space $H^2(A)$ where A is an annulus. We establish vectorriel versions of this results.

We give the vectoriel version of Hitt's result dealing with all the $S^*$ weakly invariant subspaces. We study the perturbation of a contraction by a finite rank.

The second part dealth with bases of reproducing kernels on De Branges-Rovnyak spaces thanks to Sz-nagy Foias model.
The last problem is to caracterise the operators $T\in \LL(\HH)$ complexe-symmetric. We give many exemples.
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https://tel.archives-ouvertes.fr/tel-00118743
Contributor : Nicolas Chevrot <>
Submitted on : Wednesday, December 6, 2006 - 12:18:52 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:13 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:54:09 PM

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  • HAL Id : tel-00118743, version 1

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Nicolas Chevrot. Versions vectorielles de la description de sous-espaces invariants du shift et de bases de noyaux reproduisants dans certains espaces de fonctions holomorphes.. Mathématiques [math]. Université Claude Bernard - Lyon I, 2006. Français. ⟨tel-00118743⟩

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