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Sinclair, Allan M.,

Continuous Semigroups in Banach Algebras / Allan M. Sinclair. - Cambridge : Cambridge University Press, 1982. - 1 online resource (152 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 63 . - London Mathematical Society Lecture Note Series ; no. 63. .

Title from publisher's bibliographic system (viewed on 16 Oct 2015).

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.

ISBN: 9780511662423 (ebook)

Subjects--Topical Terms:
Banach algebras
Semigroups

LC Class. No.: QA326 / .S56 1982

Dewey Class. No.: 512/.55