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

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

Similarity:

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 n , depending on the growth of exp ( i a · t ) , t 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.

Some simple proofs in holomorphic spectral theory

Graham R. Allan (2007)

Banach Center Publications

Similarity:

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.

On Kato non-singularity

Robin Harte (1996)

Studia Mathematica

Similarity:

An exactness lemma offers a simplified account of the spectral properties of the "holomorphic" analogue of normal solvability.

Spectrum of certain Banach algebras and ∂̅-problems

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

Annales Polonici Mathematici

Similarity:

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.