A convenient setting for holomorphy
A. Kriegl, L. D. Nel (1985)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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A. Kriegl, L. D. Nel (1985)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Josef Naas, Wolfgang Tutschke (1983)
Banach Center Publications
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van Brunt, Bruce, Marshall, Jonathan C. (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Joji Kajiwara (1974)
Czechoslovak Mathematical Journal
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François Trèves (1969)
Bulletin de la Société Mathématique de France
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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.