Displaying similar documents to “Non-holomorphic functional calculus for commuting operators with real spectrum”

(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...

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.

On functional linear partial differential equations in Gevrey spaces of holomorphic functions.

Stéphane Malek (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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We investigate existence and unicity of global sectorial holomorphic solutions of functional linear partial differential equations in some Gevrey spaces. A version of the Cauchy-Kowalevskaya theorem for some linear partial q -difference-differential equations is also presented.