Displaying similar documents to “The holomorphic functional calculus as an operational calculus”

Spectral study of holomorphic functions with bounded growth

Ivan Cnop (1972)

Annales de l'institut Fourier

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This paper studies properties of a large class of algebras of holomorphic functions with bounded growth in several complex variables. The main result is useful in the applications. Using the symbolic calculus of L. Waelbroeck, it gives for instance a theorem of the “Nullstellensatz” type and approximation theorems.

Non-holomorphic functional calculus for commuting operators with real spectrum

Mats Andersson, Bo Berndtsson (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider n -tuples of commuting operators a = a 1 , ... , a n on a Banach space with real spectra. The holomorphic functional calculus for a is extended to algebras of ultra-differentiable functions on ℝ n , depending on the growth of ∥ exp ( i a · t ) ∥ , t ∈ ℝ n , when | t | → ∞ . 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.