Classical and Multilinear Harmonic Analysis 2 Volume Set
Published on 21. February 2013
Book
760 pages
978-1-107-03262-0 (ISBN)
Description
This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderon-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderon's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
Reviews / Votes
'The two-volume set under review is a worthy addition to this tradition from two of the younger generation of researchers. It is remarkable that the authors have managed to fit all of this into [this number of] smaller-than-average pages without omitting to provide motivation and helpful intuitive remarks. Altogether, these books are a most welcome addition to the literature of harmonic analysis.' Gerald B. Folland, Mathematical ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 46 mm
Weight
1340 gr
ISBN-13
978-1-107-03262-0 (9781107032620)
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Schweitzer Classification
Other editions
Complete work / Part of the work
Camil Muscalu | Wilhelm Schlag
Classical and Multilinear Harmonic Analysis
Book
01/2013
Cambridge University Press
€102.80
Shipment within 15-20 days
Camil Muscalu | Wilhelm Schlag
Classical and Multilinear Harmonic Analysis
Book
01/2013
1st Edition
Cambridge University Press
€90.20
Shipment within 15-20 days
Persons
Camil Muscalu is Associate Professor of Mathematics at Cornell University, New York. Wilhelm Schlag is Professor in the Department of Mathematics at the University of Chicago.
Content
Volume 1: Preface; Acknowledgements; 1. Fourier series: convergence and summability; 2. Harmonic functions, Poisson kernel; 3. Conjugate harmonic functions, Hilbert transform; 4. The Fourier Transform on Rd and on LCA groups; 5. Introduction to probability theory; 6. Fourier series and randomness; 7. Calderon-Zygmund theory of singular integrals; 8. Littlewood-Paley theory; 9. Almost orthogonality; 10. The uncertainty principle; 11. Fourier restriction and applications; 12. Introduction to the Weyl calculus; References; Index. Volume 2: Preface; Acknowledgements; 1. Leibniz rules and gKdV equations; 2. Classical paraproducts; 3. Paraproducts on polydiscs; 4. Calderon commutators and the Cauchy integral; 5. Iterated Fourier series and physical reality; 6. The bilinear Hilbert transform; 7. Almost everywhere convergence of Fourier series; 8. Flag paraproducts; 9. Appendix: multilinear interpolation; Bibliography; Index.