Fourier Analysis and Its Applications

Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.

• 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.

From the reviews:"This book is one in the Graduate Texts in Mathematics series published by Springer. … There is a variety of worked examples as well as 350-plus exercises … . The book is a valuable addition to the literature on Fourier analysis. It is written with more mathematical rigour than many texts … without being totally opaque to the non-specialist. … The examples at the end of each chapter are well structured and a reader working through most of them will achieve a good understanding of the topics." (Graham Brindley, The Mathematical Gazette, Vol. 90 (517), 2006)"The author … presents the results of his experiences and choices for decades of teaching courses. … The tables and formulas collected … are of great service. At the end of each chapter there is a summary section that discusses the results, gives some history, and suggests instructive exercises. We thus have a solid course on Fourier analysis and its applications interesting for students and specialists in engineering as well as for mathematicians. … I believe that the book will find numerous interested readers." (Elijah Liflyand, Zentralblatt MATH, Vol. 1032 (7), 2004)"This book is an interesting mixture of a traditional approach … and a more modern one, emphasizing the role of (tempered) distributions and the application aspects of Fourier analysis. … The book is certainly highly recommendable for those who want to learn the essence of Fourier analysis in a mathematically correct way without having to go through too much technical details." (H.G. Feichtinger, Monatshefte für Mathematik, Vol. 143 (2), 2004)"The book is appropriate for an advanced undergraduate or a master’s level one-term introductory course on Fourier series with applications to boundary value problems. … a deep idea is presented in a non-rigorous way both to show the usefulness of the idea and to stimulate interest in further study. … The book has a goodcollection of exercises … . Each chapter ends with both a summary of its main results and methods and historical notes." (Colin C. Graham, Mathematical Reviews, Issue 2004 e)