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.
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1 of 1 people found the following review helpful:
5.0 out of 5 stars
Read Me first,
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This review is from: Fourier Series and Integrals (Probability and Mathematical Statistics) (Paperback)
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.
3 of 4 people found the following review helpful:
4.0 out of 5 stars
Excellent collection of diverse examples,
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This review is from: Fourier Series and Integrals (Probability and Mathematical Statistics) (Paperback)
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.)
5.0 out of 5 stars
classic but still fresh,
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This review is from: Fourier Series and Integrals (Probability and Mathematical Statistics) (Paperback)
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.
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Inside This Book
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First Sentence:
The basic idea of Fourier series is that "any" periodic function f of, say, time can be expressed as a "trigonometric sum" of sines and cosines of the same period T:. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
same double coset, perpendicular family, outer filters, summable functions, noncommutative groups, spheroidal wave functions, hyperbolic distance, spherical functions, complex function theory, double cosets, sine series, quadratic reciprocity, summation formula, prime number theorem, dual group New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The basic idea of Fourier series is that "any" periodic function f of, say, time can be expressed as a "trigonometric sum" of sines and cosines of the same period T:. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
same double coset, perpendicular family, outer filters, summable functions, noncommutative groups, spheroidal wave functions, hyperbolic distance, spherical functions, complex function theory, double cosets, sine series, quadratic reciprocity, summation formula, prime number theorem, dual group New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 54
books:
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80
books
cite this book:
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- Fourier Series by G. H. Hardy in Front Matter, and Back Matter
- Rhode Island (13 Colonies) by Roberta Wiener in Back Matter (1), and Back Matter (2)
- Brief Introduction to Theta Functions by Bellman in Back Matter
- An Introduction to Harmonic Analysis (Cambridge Mathematical Library) by Yitzhak Katznelson in Back Matter
- Complex Variables (Holden-Day Series in Mathematics) by Norman Levinson in Back Matter
See all 54 books this book cites
- Signal Analysis: Time, Frequency, Scale, and Structure by Ronald L. Allen on page 262, page 433, and page 792
- Numerical Analysis for Statisticians by Kenneth Lange on page 206, page 234, and page 251
- Exercises in Fourier Analysis by T. W. Körner on page 231, and Back Matter
- Exercises in Fourier Analysis by T. W. Körner on page 231, and Back Matter
- An Introduction to the Uncertainty Principle: Hardy's Theorem on Lie Groups (Progress in Mathematics) by Sundaram Thangavelu in Front Matter, and Back Matter
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