Functional Analysis With Applications (De Gruyter Textbook)

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study. * Covers all basic parts of functional analysis in an easy to understand way * Includes a large number of examples, exercices, and problems * Of interest to students of mathematics, physics, and engineering Cover......Page 1 Functional Analysis with Applications ......Page 5 © 2019......Page 6 Preface......Page 7 Contents ......Page 9 1 Vector, metric, normed and Banach spaces......Page 13 2 Lebesgue integration......Page 85 3 The Lp spaces......Page 191 4 Linear operators......Page 221 5 Linear functionals......Page 247 6 Relatively compact sets in metric and normed spaces. Compact operators......Page 259 7 Self-adjoint operators in Hilbert spaces......Page 277 8 The method of the small parameter......Page 285 9 The parameter continuation method......Page 311 10 Fixed-point theorems and applications......Page 321 A. Sets and mappings......Page 387 B. Functions of bounded variation......Page 397 Bibliography......Page 401 Index......Page 403

This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.