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  3. Continuous Semigroups in Banach Algebras
  • Cited by 22
Publisher:
Cambridge University Press
Online publication date:
March 2010
Print publication year:
1982
Online ISBN:
9780511662423
DOI:
https://doi.org/10.1017/CBO9780511662423
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
London Mathematical Society Lecture Note Series (63)
Information

Book description

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.

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