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

by Joseph Muscat

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.

Genres: Mathematics

431 pages, Paperback

First published June 18, 2014

Reviews

[HikBook]

This book born from the notes https://staff.um.edu.mt/jmus1/hilbert...
Hilbert spaces (see my drive)
In the notes: Problem 13 =int fgwdx with w(x) positive real function, defines an inner-product. The space is a weighted L2 space

Problem 14 Consider the vector space of holomorphic function f:RxR+->C with sup_y>0 int |f|^2then =lim_e->0 int f(x+ie)g(x+ie) dx is an inner-product