Methods of modern mathematical physics I : Functional analysis

"This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations." --Publisher description Preface ......Page 3 Introduction ......Page 5 Contents ......Page 6 1 Preliminaries......Page 13 2 Hilbert Spaces ......Page 48 3 Banach Spaces ......Page 79 4 Topological Spaces ......Page 102 5 Locally Convex Spaces ......Page 136 6 Bounded Operators ......Page 194 7 The Spectral Theorem ......Page 233 8 Unbounded Operators ......Page 261 9 The Fourier Transform ......Page 330 Supplementary Material ......Page 356 List of Symbols ......Page 405 Index ......Page 407