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.
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: June 1982
- format: Paperback
- isbn: 9780521285988
- length: 152 pages
- dimensions: 228 x 152 x 9 mm
- weight: 0.25kg
- availability: Available
Table of Contents
1. Introduction and preliminaries
2. Analytic semigroups in particular Banach algebras
3. Existence of analytic semigroups - an extension of Cohen's factorization method
4. Proof of the existence of analytic semigroups
5. Restrictions on the growth of at
6. Nilpotent semigroups and proper closed ideals
Appendix 1. The Ahlfors-Heins theorem
Appendix 2. Allan's theorem - closed ideals in L1( R+,w)
Appendix 3. Quasicentral bounded approximate identities
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email email@example.comRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×