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Title: Harmonic Analysis by Elias M. Stein, Timothy S. Murphy ISBN: 0691032165 Publisher: Princeton Univ Pr Pub. Date: 12 July, 1993 Format: Hardcover Volumes: 1 List Price(USD): $85.00 |
Average Customer Rating: 5
Rating: 5
Summary: Nothing better than learning from the experts.
Comment: If you get involved in analysis sooner or later you will have to read Elias Stein. Why? Because the core of analysis is harmonic analysis, and this man has been one of the leading experts in the field over at least 35 years, so, whatever branch of analysis you choose, Dr. Stein will be there.
This thick book (695 pages) includes most of the topics in harmonic analysis which have been researched extensively during the last 20 years. It should be taken as a complement to Stein's "Singular Integrals and Differentiability Properties of Functions" (1970) and Stein & Weiss' "Introduction to Fourier Analysis on Euclidean Spaces" (1971).
Its contents are: Real variable theory (covering lemmas, maximal function, generalized Calderón-Zygmund decomposition, etc.), maximal functions (vector-valued max. functions, Carlesson measures, etc.), Hardy spaces (characterization, atomic decomposition, singular integrals, etc.), H^1 and BMO (sharp function, interpolation, etc.), weighted inequalities (the class A_p, etc.), Fourier transform, almost orthogonality, oscillatory integrals, maximal operators, maximal averages, the Heisenberg group.
The style is concise and presents motivation for each topic. Includes excercises - called "further results" - which are short research topics on their own, and an extensive list of references. The cloth bound is lovely.
Superb book; a must in every analyst's library.
Please check my other reviews (just click on my name above).
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Title: Singular Integrals and Differentiability Properties of Functions. (PMS-30) by Elias M. Stein ISBN: 0691080798 Publisher: Princeton Univ Pr Pub. Date: 01 February, 1971 List Price(USD): $90.00 |
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Title: Trigonometric Series by A. Zygmund ISBN: 0521890535 Publisher: Cambridge Univ Pr (Pap Txt) Pub. Date: March, 2003 List Price(USD): $60.00 |
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Title: Functional Analysis by Walter Rudin ISBN: 0070542368 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 January, 1991 List Price(USD): $127.10 |
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Title: Fourier Analysis: An Introduction (Princeton Lectures in Analysis) by Elias M. Stein, Rami Shakarchi ISBN: 069111384X Publisher: Princeton Univ Pr Pub. Date: April, 2003 List Price(USD): $49.95 |
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Title: Fourier Analysis by T. W. Körner ISBN: 0521389917 Publisher: Cambridge Univ Pr (Pap Txt) Pub. Date: February, 1990 List Price(USD): $52.00 |
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