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In these notes the abstract theory of analytic one-parameter semigroups in Banach algebras is discussed, with the Gaussian, Poisson and fractional integral semigroups in convolution Banach algebras serving as motivating examples. Such semigroups are constructed in a Banach algebra with a bounded approximate identity. Growth restrictions on the semigroup are linked to the structure of the underlying Banach algebra. The Hille-Yosida Theorem and a result of J. Esterle's on the nilpotency of semigroups are proved in detail. The lecture notes are an expanded version of lectures given by the author at the University of Edinburgh in 1980 and can be used as a text for a graduate course in functional analysis.
| Introduction and preliminaries | |
| Analytic semigroups in particular Banach algebras | |
| Existence of analytic semigroups - an extension of Cohen's factorization method | |
| Proof of the existence of analytic semigroups | |
| Restrictions on growth | |
| Nilpotent semigroups and proper closed ideals | |
| Table of Contents provided by Publisher. All Rights Reserved. |
ISBN: 9780521285988
ISBN-10: 0521285984
Series: London Mathematical Society Lecture Note Series
Audience:
Professional
Format:
Paperback
Language:
English
Number Of Pages: 152
Published: 16th August 1982
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2
x 0.9
Weight (kg): 0.23
