Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax is a consideration of ideas from the point of view of spaces of homogeneous type, which culminates in a discussion of wavelets. This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.
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Book Description
Editorial Reviews
Review
Steven Krantz has written a remarkable book that leads the reader on a tour of Euclidean harmonic analysis from its genesis to the frontiers of recent research. It can be warmly recommended to professionals, graduate students, and adventurous undergraduates who want to know what this beautiful subject is about. -- Gerald Folland, University of Washington, Seattle
Book Description
This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.
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8 of 13 people found the following review helpful:
5.0 out of 5 stars
Nice guide for students and newcomers.,
This review is from: A Panorama of Harmonic Analysis (Carus Mathematical Monographs) (Hardcover)
This book is not a textbook on harmonic analysis; it is an essay on how this important discipline has evolved and what are its main results and applications.I find this book to be an excellent companion text because it includes a lot of subtle explanations that the usual textbooks lack. It is suitable also for non-mathematicians willing to get a fast introductory survey of the theory. Its contents are: Overview of Measure Theory and Functional Analysis; Fourier Series Basics; The Fourier Transform; Multiple Fourier Series; Spherical Harmonics; Fractional Integrals, Singular Integrals, and Hardy Spaces; Modern Theories of Integral Operators; Wavelets; A Retrospective; 9 appendices. Full of interesting comments and historical anecdotes. Extensive Bibliography. Please take a look at the rest of my reviews.
1 of 5 people found the following review helpful:
1.0 out of 5 stars
hackneyed,
By
This review is from: A Panorama of Harmonic Analysis (Carus Mathematical Monographs) (Hardcover)
Outside of regurgitating timeworn examples
the author does not appear to have any direction for the text. Save your money.
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
We take it for granted that the reader of this book has some acquaintance with elementary real analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
summability kernels, spherical summation, singular integral kernel, multiplier operator, homogeneous type, maximal operator, summability methods, maximal function, partial summation, bounded mean oscillation, singular integral operators, norm convergence, standard kernel, zonal harmonics, wavelet theory, fractional integrals, fractional integration, interpolation theorem, singular integrals, summation method, complete orthonormal system, dense range, operator norm Key Phrases - Capitalized Phrases (CAPs): (learn more)
Functional Analysis Principle, New Look, Quick Introduction, Daniel Bernoulli, Multi-Resolution Analysis New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
We take it for granted that the reader of this book has some acquaintance with elementary real analysis. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
summability kernels, spherical summation, singular integral kernel, multiplier operator, homogeneous type, maximal operator, summability methods, maximal function, partial summation, bounded mean oscillation, singular integral operators, norm convergence, standard kernel, zonal harmonics, wavelet theory, fractional integrals, fractional integration, interpolation theorem, singular integrals, summation method, complete orthonormal system, dense range, operator norm Key Phrases - Capitalized Phrases (CAPs): (learn more)
Functional Analysis Principle, New Look, Quick Introduction, Daniel Bernoulli, Multi-Resolution Analysis New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 62
books:
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15
books
cite this book:
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- Harmonic Analysis by Elias M. Stein on 4 pages
- Complex Analysis (Princeton Lectures in Analysis) by Elias M. Stein in Front Matter, Back Matter (1), and Back Matter (2)
- Studies in Harmonic Analysis (Mathematical Association of America. Studies in Mathematics, Vol 13) by J. Marshall Ash in Back Matter (1), and Back Matter (2)
- Complex Analysis (Lecture Notes in Mathematics) by Steven G. Krantz in Front Matter, and Back Matter
- Complex Analysis (Graduate Texts in Mathematics) by Serge Lang in Back Matter (1), and Back Matter (2)
See all 62 books this book cites
- Measures, Integrals and Martingales by René L. Schilling in Back Matter (1), and Back Matter (2)
- A Mathematician's Survival Guide: Graduate School and Early Career Development by Steven G. Krantz in Back Matter
- Handbook of Typography for Mathematical Sciences by Steven G. Krantz in Back Matter
- Differential Equations Demystified by Steven Krantz in Back Matter
- The Geometry of Domains in Space (Birkhäuser Advanced Texts Basler Lehrbücher) by Steven G. Krantz in Back Matter
See all 15 books citing this book
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