Korner T. Fourier Analysis 2022

Textbook in PDF format

Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.
Foreword by Terence Tao.
Preface.
Fourier Series.
Some Differential Equations.
Orthogonal Series.
Fourier Transforms.
Further Developments.
Other Directions.
Appendix A The circle T.
Appendix B Continuous function on closed bounded sets.
Appendix C Weakening hypotheses.
Appendix D Ode to a galvanometer.
Appendix E The principle of the argument.
Appendix F Chase the constant.
Appendix G Are share prices in Brownian motion ?
Index