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.
- ISBN13 9780521285988
- Publish Date 17 June 1982 (first published 1 January 1982)
- Publish Status Active
- Out of Print 6 June 2022
- Publish Country GB
- Imprint Cambridge University Press
- Format Paperback (US Trade)
- Pages 152
- Language English