Methods of Modern Mathematical Physics. I: Functional Analysis

Academic Press, 1972. Hardcover. First edition of Volume I, VG++/no DJ, 325pp, text is bright, clean and fresh-in NF cond Methods of Modern Mathematical Physics, Volume I: Functional Analysis discusses the fundamental principles of functional analysis in modern mathematical physics. This book also analyzes the influence of mathematics on physics, such as the Newtonian mechanics used to interpret all physical phenomena. Organized into eight chapters, this volume starts with an overview of the functional analysis in the study of several concrete models. This book then discusses how to generalize the Lebesgue integral to work with functions on the real line and with Borel sets. This text also explores the properties of finite-dimensional vector spaces. Other chapters discuss the normed linear spaces, which have the property of being complete. This monograph further examines the general class of topologized vector spaces and the spaces of distributions that arise in a wide variety of physical problems and functional situations. This book is a valuable resource for mathematicians and physicists. Students and researchers in the field of geometry will also find this book extremely useful. Content: Front Matter , Page iii Copyright , Page iv Dedication , Page v Preface , Page vii Introduction , Pages ix-xi Contents of Other Volumes , Page xvii I - Preliminaries , Pages 1-35 II - Hilbert Spaces , Pages 36-66 III - Banach Spaces , Pages 67-89 IV - Topological Spaces , Pages 90-123 V - Locally Convex Spaces , Pages 124-181 VI - Bounded Operators , Pages 182-220 VII - The Spectral Theorem , Pages 221-248 VIII - Unbounded Operators , Pages 249-317 List of Symbols , Pages 319-320 Index , Pages 321-325 v. 1. Functional analysis. v. 2. Fourier analysis, self-adjointness. v. 3. Scattering theory. v. 4. Analysis of operators.