Written by a successful author and respected mathematician, this book emphasizes a concrete and computational approach to the subject of Fourier analysis and wavelet theory while maintaining a balance between theory and applications. In some cases, several different proofs are offered for a given proposition, allowing students to compare different methods.
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Most Helpful Customer Reviews
5 of 6 people found the following review helpful:
5.0 out of 5 stars
Fourier Analysis and Wavelets for Everyone,
This review is from: Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics) (Hardcover)
As a probabilist and statistician, with a Ph.D., having worked at universities, as a consultant, and in industry for approximately forty years, I had previously employed Fourier Analysis only as a tool, not having studied the subject as a discipline unto itself. Dr. Pinsky's book has allowed me to learn the subject more deeply, and from a different, exciting viewpoint. In addition, I needed a resource that would permit me to learn about wavelets. How wonderful to find a book that includes both topics! Moreover, this book is a pleasure to read, with pencil and paper, to work through the ideas. It is extraordinarily well-written, which is not surprising, given the clarity and excellence of Dr. Mark A. Pinsky's other works. Pinsky's grammar is excellent, which is extremely refreshing. Many modern authors cause me to believe that I should have a red pen to correct grammatical errors while reading their works. This book is much more than just a textbook; it is beautiful mathematically and beautifully written.
8 of 12 people found the following review helpful:
5.0 out of 5 stars
For the Students!,
By Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews (VINE VOICE) (REAL NAME)
This review is from: Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics) (Hardcover)
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.
1 of 6 people found the following review helpful:
5.0 out of 5 stars
Excellent textbook and reference, which is readable!,
This review is from: Introduction to Fourier Analysis and Wavelets (Brooks/Cole Series in Advanced Mathematics) (Hardcover)
I needed to learn Fourier Analysis and Wavelets, and this book is excellent as a textbook and as a reference. It is also quite readable. We need more mathematics books like this one.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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continuum wavelet, periodic heat kernel, absolutely convergent trigonometric series, spherical partial sum, summability matrix, scaling function satisfies, nonnegative harmonic function, dilation matrix, scaling filter, approximate identity, integer translates, differentiation theorem, trigonometric approximation, scaling equation, wavelet series, final integral, maximal function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Lemma, The de la Vallée Poussin, Borel-Cantelli Lemma, Orthonormal Translates Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
continuum wavelet, periodic heat kernel, absolutely convergent trigonometric series, spherical partial sum, summability matrix, scaling function satisfies, nonnegative harmonic function, dilation matrix, scaling filter, approximate identity, integer translates, differentiation theorem, trigonometric approximation, scaling equation, wavelet series, final integral, maximal function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Lemma, The de la Vallée Poussin, Borel-Cantelli Lemma, Orthonormal Translates Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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