Fourier Analysis and Its Applications

1. Auflage 2003. Corr. 2. printing 2005
ISBN: 978-0-387-00836-3
Verlag: Springer

Buch, Englisch, 272 Seiten, Format (B × H): 161 mm x 241 mm, Gewicht: 1280 g

Reihe: Graduate Texts in Mathematics

A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include 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 does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

Zielgruppe

Graduate

Autoren/Hrsg.

Vretblad, Anders

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.

Über Autor(innen)

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