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.
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.
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.