A Treatise on Trigonometric Series
eBook - PDF

A Treatise on Trigonometric Series

Volume 1

  1. 578 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

A Treatise on Trigonometric Series

Volume 1

Book details
Table of contents
Citations

About This Book

A Treatise on Trigonometric Series, Volume 1 deals comprehensively with the classical theory of Fourier series. This book presents the investigation of best approximations of functions by trigonometric polynomials. Organized into six chapters, this volume begins with an overview of the fundamental concepts and theorems in the theory of trigonometric series, which play a significant role in mathematics and in many of its applications. This text then explores the properties of the Fourier coefficient function and estimates the rate at which its Fourier coefficients tend to zero. Other chapters consider some tests for the convergence of a Fourier series at a given point. This book discusses as well the conditions under which the series does converge uniformly. The final chapter deals with adjustment of a summable function outside a given perfect set. This book is a valuable resource for advanced students and research workers. Mathematicians will also find this book useful.

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Information

Publisher
Pergamon
Year
2014
ISBN
9781483224190
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. A Treatise on Trigonometric Series
  3. Copyright Page
  4. Table of Contents
  5. CONTENTS OF VOLUME II
  6. TRANSLATOR'S PREFACE
  7. AUTHOR'S PREFACE
  8. NOTATION
  9. INTRODUCTORY MATERIAL
  10. CHAPTER I. BASIC CONCEPTS AND THEOREMS IN THETHEORY OF TRIGONOMETRIC SERIES
  11. CHAPTER II. FOURIER COEFFICIENTS
  12. CHAPTER III. THE CONVERGENCE OF A FOURIER SERIES AT A POINT
  13. CHAPTER IV. FOURIER SERIES OF CONTINUOUS FUNCTIONS
  14. CHAPTER V. CONVERGENCE AND DIVERGENCE OF A FOURIER SERIES IN A SET
  15. CHAPTER VI. "ADJUSTMENT" OF FUNCTIONS IN A SET OF SMALL MEASURE
  16. APPENDIX TO CHAPTER II
  17. APPENDIX TO CHAPTER IV
  18. APPENDIX TO CHAPTER V
  19. BIBLIOGRAPHY
  20. INDEX