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A GENERAL FRAMEWORK FOR HOLOMORPHIC FUNCTIONAL CALCULI

Published online by Cambridge University Press:  23 May 2005

Markus Haase
Markus Haase
Affiliation:
Abteilung Angewandte Analysis, Universität Ulm, Helmholtzstra\ss{e} 18, 89069 Ulm, Germany (haase@mathematik.uni-ulm.de)
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Abstract

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We present an abstract approach to the construction of holomorphic functional calculi for unbounded operators and apply it to the special case of sectorial operators. In effect, we obtain a calculus for a much larger class of functions than was known before, including certain meromorphic functions. We discuss the role of topology. Then we prove in detail a composition rule $(f\circ g)(A)=f(g(A))$ which is the main result of the paper. This is done in such a way that the proof can easily be transferred to functional calculi for other classes of operators.

Keywords

Primary 47A6047D06functional calculussectorial operatorholomorphic semigroup
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 2 , June 2005 , pp. 423 - 444
Copyright
Copyright © Edinburgh Mathematical Society 2005