Author | Vretblad, Anders. author |
---|---|

Title | Fourier Analysis and Its Applications [electronic resource] / by Anders Vretblad ; edited by S. Axler, F. W. Gehring, K. A. Ribet |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2003 |

Connect to | http://dx.doi.org/10.1007/b97452 |

Descript | XII, 272 p. online resource |

SUMMARY

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

CONTENT

Introduction -- Preparations -- Laplace and Z Transforms -- Fourier Series -- L̂2 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

Mathematics
Fourier analysis
Mathematics
Fourier Analysis