2009•Unpublished venueRequires access

Unbounded operators: functional calculus, generation, perturbations

C. J. K. Batty

Abstract

These lectures review the H1-functional calculus of sectorial operators and related\nclasses of unbounded operators. Their theory is related to the well established theory of C0-\nsemigroups and cosine functions. In most cases the existence of a bounded H1-calculus\nis equivalent to certain quadratic estimates arising from harmonic analysis. In addition to\ndescribing the topic in general, the lectures include recent results in perturbation theory for\nfunctional calculus and for di®erentiable semigroups.

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Key concepts: Functional calculus, Mathematics, Time-scale calculus, Holomorphic functional calculus, Calculus (dental), Operator theory, Algebra over a field, Bounded function