Classical and multilinear harmonic analysis [electronic resource] / Camil Muscalu , Cornell University, Wilhelm Schlag, University of Chicago.
"This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained, and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the...
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| Language: | English |
| Published: |
Cambridge, UK :
Cambridge University Press,
2013.
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| Series: | Cambridge studies in advanced mathematics ;
137-138 |
| Subjects: | |
| Online Access: | |
| Format: | Electronic eBook |
Contents:
- v.1. Fourier series: convergence and summability ; Harmonic functions; Poisson kernel ; Conjugate harmonic fuctions; Hilbert transform ; The Fourier transform on R[superscript d] and on LCA groups ; Introduction to probability theory ; Fourier series and randomness ; Calderâon-Zygmund theory of singular integrals ; Littlewood-Paley theory ; Almost orthogonality ; The uncertainty principle ; Fourier restriction and applications ; Introduction to the Weyl calculus
- v. 2. Leibnitz rules and the generalized Korteweg-de Vries equation ; Classical paraproducts ; Paraproducts on polydisks ; Calderâon commutators and the Cauchy integral on Lipschitz curves ; Iterated Fourier series and physical reality ; The bilinear Hilbert transform ; Almost everywhere convergence of Fourier series ; Flag paraproducts ; Appendix: multilinear interpolation.