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Problèmes d'Interpolation dans les Espaces de Paley-Wiener et Applications en Théorie du Contrôle

Abstract : We study interpolation problems in spaces of analytic functions and in particular in Paley-Wiener spaces.We show that the restriction operator associated to some N-Carleson sequence is an isomorphism between the Paley-Wiener space and a certain space of sequences (contructed with the help of divided differences) if and only if the sequence satisfies some conditions, in particular the Muckenhoupt condition. This result is a generalization of a theorem of Lyubarskii and Seip obtained in 1997.We also show that every minimal sequence in PW such that the intersection with every half-plane satisfies the Carleson condition is actually an interpolating sequence in every "bigger" space in the sense of the exponential type. This result can be extended to weighted interpolation and has an application in Control Theory.
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https://tel.archives-ouvertes.fr/tel-00652210
Contributor : Frederic Gaunard <>
Submitted on : Thursday, December 15, 2011 - 10:04:17 AM
Last modification on : Thursday, January 11, 2018 - 6:21:22 AM
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Gaunard Frédéric. Problèmes d'Interpolation dans les Espaces de Paley-Wiener et Applications en Théorie du Contrôle. Analyse fonctionnelle [math.FA]. Université Bordeaux I, 2011. Français. ⟨NNT : 2011BOR14371⟩. ⟨tel-00652210⟩

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