Introduction to Fourier Analysis and Wavelets (Graduate Studies in Mathematics) by Mark A. Pinsky (PDF)

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Mark A. Pinsky

User’s Reviews

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

⭐This is a delightful book. To read it one needs first to have studied measure theory. The book gives a clean presentation of wavelets and is probably the best place to learn about them. It also has a good chapter on applications of Fourier analysis in probability theory: the central limit theorem, a result on “gap series”, the Berry-Esséen theorem, and the law of the iterated logarithm. The other chapters cover the usual material in a course on Fourier analysis, and more. The proofs are tidy and computational, but that does not mean they are shallow- for example Pinsky has many things to say about radial functions and this involves Bessel functions, which never appear in Katznelson. Some other topics this book covers well that are often not mentioned: Hermite polynomials, spherical Fourier inversion, applications of lattice point counting. It does not talk about locally compact abelian groups, Banach algebras, or the Gelfand transform, but it has results particular to Euclidean spaces like singular integrals.

⭐Courses in harmonic analysis have a central place in the course offerings of every math department, be it pure or applied;– and the subject is as important as ever! Yet it has not always been easy for an instructor to find a book that is right for the students. Some books might be too skimpy on proofs, or not deep enough.– Or the applications may somehow be artificial, or contrived. Afterall, we teach the material to engineers!– It is a relief to find, in Pinsky’s lovely new book, a balanced approach to the subject. The motivation and the history receive a beautiful presentation, as do the technical points and proofs. And the historical comments- sprinkled throughout the book- bring the subject to life. At the same time, the book is forward looking, and it has been tested in courses. Great exercises! The structure of the exposition is friendly, and gently leads the reader toward the exciting new wavelet material in the last hundred or so pages of the book. The student thereby gets a sense of how the central questions in wavelet theory have their root in the more classical ideas of harmonic analysis.

⭐Not found.

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