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.
Author(s): Svetlin G. Georgiev, Khaled Zennir
Publisher: De Gruyter
Year: 2019
Language: English
Pages: 406
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
