Reed M., Simon B. - Methods of modern mathematical physics. Functional analysis Vol. 1
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. This revised and enlarged edition differs from the first in two major ways. First, many colleagues have suggested to us that it would be helpful to include some material on the Fourier transform in Volume I so mat this important topic can be conveniently included in a standard functional analysis course using this book. Thus, we have included in this edition Sections IX. 1, IX.2, and part of IX.3 from Volume II and some additional material, together with relevant notes and problems. По-друге, we have included a variety of supplementary material at the end of the book. Some of these supplementary sections provide proofs of theorems in Chapters II-IV which were omitted in the first edition. While these proofs make Chapters II-IV more self-contained, we still recommend that students with no previous experience with this material consult more elementary texts. Other supplementary sections provide expository material to aid the instructor and the student (for example, "Applications of Compact Operators"). Still other sections introduce and develop new material (for example, "Minimization of Functional"). It gives us pleasure to thank many individuals: The students who took our course in 1970-1971 and especially J. E. Taylor for constructive comments about the lectures and lecture notes. L. Gross, T. Kato, and especially D. Ruelle for reading parts of the manuscript and for making numerous and suggestions corrections..