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

Mats Andersson (2003)

Annales de l’institut Fourier

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 of a . If a ...

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