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Fourier Analysis and Its Applications

Fourier Analysis and Its Applications
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Field name Details
Dewey Class 515.2433
Title Fourier Analysis and Its Applications ([EBook]) / by Anders Vretblad ; edited by S. Axler, F. W. Gehring, K. A. Ribet.
Author Vretblad, Anders
Added Personal Name Axler, Sheldon
Gehring, F. W.
Ribet, K. A.
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 2003.
Physical Details XII, 272 pages : online resource.
Series Graduate texts in mathematics 0072-5285 ; ; 223
ISBN 9780387217239
Summary Note This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time, he has included discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually will not find in books at this level. Many of the chapters end with a summary of their contents, as well as a short historical note. The text contains a great number of examples, as well as more than 350 exercises. In addition, one of the appendices is a collection of the formulas needed to solve problems in the field. Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.:
Contents note Introduction -- Preparations -- Laplace and Z Transforms -- Fourier Series -- L 2 Theory -- Separation of Variables -- Fourier Transforms -- Distributions -- Multi-Dimensional Fourier Analysis -- Appendix A: The ubiquitous convolution -- Appendix B: The Discrete Fourier Transform -- Appendix C: Formulae -- Appendix D: Answers to exercises -- Appendix E: Literature.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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