Description
Book SynopsisThis two-volume text in harmonic analysis is appropriate for advanced undergraduate students with a strong background in mathematical analysis and for beginning graduate students wishing to specialize in analysis. With numerous exercises and problems it is suitable for independent study as well as for use as a course text.
Trade ReviewReview of the set: '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
Table of ContentsPreface; 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.
