Integral representation of functions on sectors, functional calculus and norm estimates.

Khristo N. Boyadzhiev

Displaying similar documents to “Integral representation of functions on sectors, functional calculus and norm estimates.”

A constructive proof of the composition rule for Taylor's functional calculus

Mats Andersson, Sebastian Sandberg (2000)

Studia Mathematica

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We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.

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 $∥ exp (i a \cdot t) ∥$ , $t \in ℝ^{n}$ , when $| t | \to \infty$ . 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.

(Ultra)differentiable functional calculus and current extension of the resolvent mapping

Mats Andersson (2003)

Annales de l’institut Fourier

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Let $a = (a_{1}, ..., a_{n})$ be a tuple of commuting operators on a Banach space $X$ . 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...

Functional calculus for generators of uniformly bounded holomorphic semigroups.

Ralph de Laubenfels (1989)

Semigroup forum

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Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators.

deLaubenfels, Ralph, Lei, Yansong (1997)

Abstract and Applied Analysis

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Representation generated by a finite number of Hilbert space operators

Marek Kosiek (1984)

Annales Polonici Mathematici

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A note on normal operators

B. S. Yadav, P. B. Ramanujan (1969)

Matematički Vesnik

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On the differentiability of Urysohn and Nemyckii operators

Jiří Durdil (1967)

Commentationes Mathematicae Universitatis Carolinae

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Automatic extensions of functional calculi

Ralph deLaubenfels (1995)

Studia Mathematica

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Given a Banach algebra ℱ of complex-valued functions and a closed, linear (possibly unbounded) densely defined operator A, on a Banach space, with an ℱ functional calculus we present two ways of extending this functional calculus to a much larger class of functions with little or no growth conditions. We apply this to spectral operators of scalar type, generators of bounded strongly continuous groups and operators whose resolvent set contains a half-line. For f in this larger class,...