Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté. Image fixe : sans médiation
Auteur(s) : Muscalu, Camil
Schlag, Wilhelm
Titre(s) : Classical and multilinear harmonic analysis [Texte imprimé] / Camil Muscalu,... Wilhelm Schlag,...
Publication : Cambridge : Cambridge university press, 2013
Description matérielle : 2 vol. (XVIII-370, XVI-324 p.) : ill. ; 24 cm
Collection : Cambridge studies in advanced mathematics ; 137-138
Lien à la collection : Cambridge studies in advanced mathematics
Comprend : 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.
Note(s) : Notes bibliogr.
"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 classroom alike. This 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"--
Sujet(s) : Analyse harmonique (mathématiques)
Indice(s) Dewey :
515.24 (23e éd.) = Suites et séries (mathématiques)
Identifiants, prix et caractéristiques : ISBN 9780521882453. - ISBN 0521882451 (vol. 1). - ISBN 9781107031821. - ISBN 1107031826
(vol. 2) (rel.). - ISBN 1107032628. - ISBN 9781107032620 (éd. complète)
Identifiant de la notice : ark:/12148/cb435330870
Notice n° :
FRBNF43533087
(notice reprise d'un réservoir extérieur)
