Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras - Brossura

Muscat, Joseph

Brossura

ISBN 10: 3319067273 ISBN 13: 9783319067278

Casa editrice: Springer, 2014

Riassunto

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should appeal not only to mathematicians interested in applications, but also to researchers in related fields.

Functional Analysis adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, based upon the classical sequence and function spaces and their operators. It assumes only a minimum of knowledge in elementary linear algebra and real analysis; the latter is redone in the light of metric spaces. It contains more than a thousand worked examples and exercises, which make up the main body of the book.

Su questo libro

L'autore

Professor Joseph Muscat graduated at the University of Oxford and obtained his Ph.D. from Princeton University with a thesis on the Maxwell-Klein-Gordon equation on curved space-time. He has written several papers on the applications of functional analysis to inverse problems in the biomedical field and is a co-author of the novel ACSP method in EEG signal processing.

Contenuti

Introduction.- Distance.- Convergence and Continuity.- Completeness and Separability.- Connectedness.- Compactness.- Normed Spaces.- Continuous Linear Maps.- Main Examples.- Hilbert Spaces.- Banach Spaces.- Differentiation and Integration.- Banach Algebras.- Spectral Theory.- C∗-Algebras.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2014
• ISBN 10: 3319067273
• ISBN 13: 9783319067278
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 432