Abstract
We convey the fundamental intuition behind the concept “functional calculus” (Section 1.1). Then we present a formalisation of certain ideas common to many functional calculus constructions. In particular, we introduce a method of extending an elementary functional calculus to a larger algebra (Section 1.2). In Section 1.3 we introduce the notion of a meromophic functional calculus for a closed operator A on a Banach space and specialise the abstract results from Section 1.2. As an important example we treat multiplication operators (Section 1.4). In Section 1.3.2 we prove an abstract composition rule for a pair of meromorphic functional calculi.
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© 2006 Birkhäuser Verlag
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Haase, M. (2006). Axiomatics for Functional Calculi. In: The Functional Calculus for Sectorial Operators. Operator Theory: Advances and Applications, vol 169. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7698-8_1
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DOI: https://doi.org/10.1007/3-7643-7698-8_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7697-0
Online ISBN: 978-3-7643-7698-7
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