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dc.contributor.authorPETKOVA, Violeta
dc.date2005-12-14
dc.date.accessioned2021-01-13T14:03:03Z
dc.date.available2021-01-13T14:03:03Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/25169
dc.description.abstractOn considère les multiplicateurs (les opérateurs bornés qui commutent avec les translations) sur un espace de Banach de fonctions sur un groupe G localement compact abélien. On démontre que grâce à une transformation de Fourier généralisée, on peut associer à chaque multiplicateur un symbole essentiellement borné sur un sous-ensemble convenable des morphismes continus de G dans C. On généralise ainsi des résultats bien connus dans les espaces L^p(G), pour p supérieur à 1 et strictement inférieur à l'infini.
dc.description.abstractEnA bounded operator M is called multiplier if M commutes with the translations. It is well known that for every multiplier on Lρ(G) (1 ≤ ρ < +∞), there exists hM ∈ L∞(0) such that Mf = hmf, ∀f ∈ Cc(G), where ĝ is the Fourier transform of g. We generalize this result. First we consider the multipliers on weighted spaces on ℝ and we obtain that every multiplier has a L∞ or H∞ symbol on a complex strip related to the spectrum of the shift. We also prove a representation theorem for Wiener-Hopf operators on weighted spaces on ℝ+. Next, we consider the multipliers (resp. Toeplitz operators ) on very general Banach spaces of sequences on ℤ (resp. ℤ+). Finally, we consider an abstract setup and we are interested to study the multipliers on Banach spaces of functions on a locally compact abelian group G satisfying some weak conditions. We prove that for every bounded operator M commuting with translations there exists hM ∈ L∞(GE) such that Mf = hm f, ∀f ∈ Cc(G), where 6E is a suitable subset of the group of the continuous morphisms from G into C* and -,g- is a generalized Fourier transform of g defined on GE.
dc.formatapplication/pdf
dc.languagefr
dc.rightsfree
dc.subjectMathématiques Pures
dc.subjectmultiplicateurs
dc.subjectshift
dc.subjecttransformée de Fourier
dc.subjecttranslations
dc.titleMultiplicateurs dans les espaces de Banach de fonctions sur un groupement localement compact Abélien.
dc.typeThèses de doctorat
bordeaux.hal.laboratoriesThèses Bordeaux 1 Ori-Oai*
bordeaux.institutionUniversité de Bordeaux
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.title=Multiplicateurs%20dans%20les%20espaces%20de%20Banach%20de%20fonctions%20sur%20un%20groupement%20localement%20compact%20Ab%C3%A9lien.&amp;rft.atitle=Multiplicateurs%20dans%20les%20espaces%20de%20Banach%20de%20fonctions%20sur%20un%20groupement%20localement%20compact%20Ab%C3%A9lien.&amp;rft.au=PETKOVA,%20Violeta&amp;rft.genre=unknown


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