Fourier Series and Integrals (Probability and Mathematical Statistics) by H. Dym (PDF)

Description

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier’s basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This classic text reads as well now as it did 15 yearsago when I read it as graduate student. Should be accessibleto better undergraduates but everyone interested in mathematicscan take pleasure in this presentation of a wide variety of topicsin basic Fourier theory together with interesting applications.But note that this book is not an introduction to current researchin harmonic analysis. For that one should look at books by Steinand others. Nonetheless, this is a beautiful introduction thebasic theory.

⭐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.)

⭐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.

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