Customer Reviews

Fourier Series and Integrals (Probability and Mathematical Statistics)

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If you want to learn harmonic analysis. Very concrete and lucid, and tells you what harmonic analysis is for. You can then go on to more abstract texts. Or not. Sadly appears out of print (or just insanely overpriced) at this writing.

If you want a diverse collection of examples of the many different kinds of applications of the theory of Fourier series and Fourier integrals, you could hardly do better than this book. These include not only wave motion and heat flow (covered in every textbook), but also: the central limit theorem, the geometry of numbers, the isoperimetric problem, Heisenberg's inequality, recurrence of random walks, quadratic reciprocity, and many others.

(This book also explains the theory of measure and integration from scratch, but do not assume that this is the best place to learn that subject for the first time; the treatment of that topic is rather terse.)

This classic text reads as well now as it did 15 years
ago when I read it as graduate student. Should be accessible
to better undergraduates but everyone interested in mathematics
can take pleasure in this presentation of a wide variety of topics
in basic Fourier theory together with interesting applications.
But note that this book is not an introduction to current research
in harmonic analysis. For that one should look at books by Stein
and others. Nonetheless, this is a beautiful introduction the
basic theory.