The scope and history of commutative and noncommutative harmonic analysis / George W. Mackey.

Format:

Book

Author/Creator:

Mackey, George W. (George Whitelaw), 1916-2006, author.

Series:

History of mathematics ; Volume 5.

History of Mathematics ; Volume 5

Language:

English

Subjects (All):

Harmonic analysis--History.

Harmonic analysis.

Physical Description:

1 online resource (371 pages) : illustrations.

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society : London Mathematical Society, 1992.

Summary:

"When I was invited to speak at the conference on the history of analysis given at Rice University [in 1977], I decided that it might be interesting to review the history of mathematics and physics in the last three hundred years or so with heavy emphasis on those parts in which harmonic analysis had played a decisive or at least a major role. I was pleased and somewhat astonished to find how much of both subjects could be included under this rubric … The picture that gradually emerged as the various details fell into place was one that I found very beautiful, and the process of seeing it do so left me in an almost constant state of euphoria. I would like to believe that others can be led to see this picture by reading my paper, and to facilitate this I have included a large number of short expositions of topics which are not widely understood by non-specialists." -from the Preface This volume, containing the paper mentioned above as well as five other reprinted papers by Mackey, presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. A seventh paper, written exclusively for this volume, attempts to unify certain themes that emerged after major discoveries in 1967 and 1968 in the areas of Lie algebras, strong interaction physics, statistical mechanics, and nonlinear partial differential equations-discoveries that may at first glance appear to be independent, but which are in fact deeply interrelated.

Contents:

Cover

Title page

Contents

Introduction

Harmonic analysis as the exploitation of symmetry: A historical survey

Herman Weyl and the application of group theory to quantum mechanics

The significance of invariant measures for harmonic analysis

Weyl's program and modern physics

Induced representations and the applications of harmonic analysis

Von Neumann and the early days of ergodic theory

Final remarks

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Consists of six reprinted articles originally written as expanded versions of talks given at various conferences and published between 1978 and 1990.

ISBN:

1-4704-3873-9