Classical and Multilinear Harmonic Analysis 2 Volume Set
Classical and Multilinear Harmonic Analysis 2 Volume Set
£108.00
GBPThis 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 Calderón–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; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.
- Provides a solid foundation for beginning graduate students
- Covers more material than the average introductory text
- Suitable for students and teachers alike
Reviews & endorsements
'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 Reviews
Product details
February 2013Multiple copy pack
9781107032620
760 pages
234 × 156 × 46 mm
1.34kg
Temporarily unavailable - available from TBC
Table of Contents
- 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. Calderón–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. Calderón 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.
