This edition develops the basic theory of Fourier transform. Stroock's approach is the one taken originally by Norbert Wiener and the Parseval's formula, as well as the Fourier inversion formula via Hermite functions. New exercises and solutions have been added for this edition.

Review

"This is a very attractive textbook... Unusual in many respects, [it] fully achieves its goal, a one-semester, concise but logically complete treatment of abstract integration. It is remarkable that [the author] has accomplished so much in so short a compass."

- Mathematical Reviews (review of the first edition)

"A number of valuable applications and a good collection of problems... A very interesting, well-informed book which draws on recent approaches not found in several commonly used texts."

- Zentralblatt Math (review of the second edition)

"The author succeeded in choosing the right level of generality and showed how a good combination of a measure and integration course and advanced calculus can be done. Strongly recommended to students as well as to teachers."

- EMS Newsletter (review of the second edition)

"...the author is a distinguished probabilist/analyst who has made seminal contributions to the interface of probability theory with PDEs/harmonic analysis/functional analysis; the flavor of all these subjects is brought out in the book, especially in chapters V-VII...[the] book can be highly rewarding, serving as a launching pad for an intensive study of any branch of analysis including probability theory."

--Current Science (review of the third edition)

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