Spectral study of holomorphic functions with bounded growth

Ivan Cnop

Displaying similar documents to “Spectral study of holomorphic functions with bounded growth”

The holomorphic functional calculus as an operational calculus

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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.

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Graham R. Allan (2007)

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This paper gives some very elementary proofs of results of Aupetit, Ransford and others on the variation of the spectral radius of a holomorphic family of elements in a Banach algebra. There is also some brief discussion of a notorious unsolved problem in automatic continuity theory.

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L. Waelbroeck (1983)

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Robin Harte (1996)

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

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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.

Spectrum of certain Banach algebras and ∂̅-problems

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

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We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.