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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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There is much focus on California, but much of the information can be used in other eaaster and mid-western states for setting up a business.
I highly reccomend this book as a guide to help one build a success paralegal business.
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This book is one component of the Stein trilogy on harmonic analysis (together with "Singular Integrals and Differentiability Properties of Functions" and "Harmonic Analysis", both also reviewed by myself), and as such it must be regarded as an authoritative reference on the subject since Elias Stein and Guido Weiss are two of the leading experts in the field, and the material they selected was taken from their teaching and research experience.
The contents of the book are: The Fourier Transform; Boundary Values of Harmonic Functions; The Theory of H^p Spaces on Tubes; Symmetry Properties of the Fourier Transform; Interpolation of Operators; Singular Integrals and Systems of Conjugate Harmonic Functions; Multiple Fourier Series.
Includes motivation and full explanations for each topic, excercises for each chapter, called "further results", and extensive references. Outstanding printing quality and nice clothbound.
These three volumes should be present in every analyst's library.
Please take a look to the rest of my reviews (just click on my name above).
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Beginning with Alexander the Great and running through the beginning of the Common Era, the book is organized roughly chronologically and by theme. Chapters treat in some detail such important issues as the Septuagint, the Jewish communities in the Diaspora, Aramaic literature, Jewish religious practices, the economy of Palestine during the period, the development of priestly and scribal classes, etc.
Bickerman's prose is elegant and readable without sacrificing detail, and a substantial bibliography organized by subject provides a great starting point for further research into specific questions. You'll want to read this in connection with any study of the Deuterocanonical books, the Pseudepigrapha or the Dead Sea Scrolls, or even as a useful bridge between study of the Old Testament and the New.
Thanking you,
Olusoji Elias.