Notes on the Taylor joint spectrum of commuting operators
R. Levi (1982)
Banach Center Publications
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R. Levi (1982)
Banach Center Publications
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Mats Andersson, Bo Berndtsson (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We consider -tuples of commuting operators on a Banach space with real spectra. The holomorphic functional calculus for is extended to algebras of ultra-differentiable functions on , depending on the growth of , , when . In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.
Mats Andersson (2003)
Annales de l’institut Fourier
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Let be a tuple of commuting operators on a Banach space . We discuss various conditions equivalent to that the holomorphic (Taylor) functional calculus has an extension to the real-analytic functions or various ultradifferentiable classes. In particular, we discuss the possible existence of a functional calculus for smooth functions. We relate the existence of a possible extension to existence of a certain (ultra)current extension of the resolvent mapping over the (Taylor) spectrum...
Khristo N. Boyadzhiev (2002)
Collectanea Mathematica
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L. Waelbroeck (1982)
Banach Center Publications
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François Trèves (1969)
Bulletin de la Société Mathématique de France
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V. Müller (2002)
Studia Mathematica
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We give a Martinelli-Vasilescu type formula for the Taylor functional calculus and a simple proof of its basic properties.
M. Putinar (1984)
Studia Mathematica
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Stéphane Malek (2007)
Annales de la faculté des sciences de Toulouse Mathématiques
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We investigate existence and unicity of global sectorial holomorphic solutions of functional linear partial differential equations in some Gevrey spaces. A version of the Cauchy-Kowalevskaya theorem for some linear partial -difference-differential equations is also presented.