A Treatise on Trigonometric Series: Volume 1, المجلد 1Elsevier, 12/05/2014 - 578 من الصفحات 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. |
المحتوى
| 1 | |
CHAPTER I BASIC CONCEPTS AND THEOREMS IN THETHEORY OF TRIGONOMETRIC SERIES | 43 |
CHAPTER II FOURIER COEFFICIENTS | 209 |
CHAPTER III THE CONVERGENCE OF A FOURIER SERIES AT A POINT | 260 |
CHAPTER IV FOURIER SERIES OF CONTINUOUS FUNCTIONS | 296 |
CHAPTER V CONVERGENCE AND DIVERGENCE OF A FOURIER SERIES IN A SET | 362 |
CHAPTER VI ADJUSTMENT OF FUNCTIONS IN A SET OF SMALL MEASURE | 488 |
APPENDIX TO CHAPTER II | 528 |
APPENDIX TO CHAPTER IV | 532 |
APPENDIX TO CHAPTER V | 536 |
| 537 | |
| 549 | |
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عبارات ومصطلحات مألوفة
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