Classical and multilinear harmonic analysis / Camil Muscalu, Wilhelm Schlag

• Autore: Muscalu, Camil
• Pubblicazione: Cambridge, UK : Cambridge University Press, 2013
• Descrizione fisica: 2 v. : il. ; 24 cm
• Disciplina: 515.2422
• Soggetto topico: Harmonic analysis
• Classificazione: AMS 42-02; LC QA403
• Altri autori: Schlag, Wilhelmauthor
• Nota di bibliografia: Includes bibliographical references and indexes
• Nota di contenuto: 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 ; Calderón-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 ; Calderón 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
• Sommario/riassunto: "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 commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form": Provided by publisher
• ISBN: 9780521882453 (v. 1 : hardback); 0521882451 (v. 1 : hardback); 9781107031821 (v. 2 : hardback); 1107031826 (v. 2 : hardback); 1107032628 (set)
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 991002667559707536
• Lo trovi qui: Univ. del Salento
• Localizzazioni e accesso elettronico: http://assets.cambridge.org/97805218/82453/cover/9780521882453.jpg
• Serie: Cambridge studies in advanced mathematics ; 137-138