Continuous semigroups in Banach algebras
By: Allan M. Sinclair.
Series: London Mathematical Society lecture note series ;; 63
Publisher: Cambridge University Press
Published: 1982
Place of publication: Cambridge [Cambridgeshire]; New York
Language: eng
Number of pages: 145
Subjects: Banach algebras.; Semigroups.
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.
Notes: Bibliography: p. 138-142.
Includes index.