Harmonic Analysis on Symmetric Spaces and Applications I

  • Audrey Terras

Table of contents

  1. Front Matter
    Pages i-xv
  2. Audrey Terras
    Pages 1-82
  3. Audrey Terras
    Pages 83-119
  4. Audrey Terras
    Pages 120-320
  5. Back Matter
    Pages 301-341

About this book

Introduction

Since its beginnings with Fourier (and as far back as the Babylonian astron­ omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli­ cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.

Keywords

Analysis Fourier series Koordinatentransformation Spaces boundary element method diophantine equation distribution equation fourier analysis generalized function harmonic analysis integral medicine metric space zeta function

Authors and affiliations

  • Audrey Terras
    • 1
  1. 1.Department of Mathematics C-012University of California at San DiegoLa JollaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5128-6
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96159-0
  • Online ISBN 978-1-4612-5128-6
  • About this book