Singular Integrals in Quantum Euclidean Spaces

• Autore: González-Pérez Adrían M
• Pubblicazione: Providence : , : American Mathematical Society, , 2021; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (110 pages)
• Disciplina: 515/.723
• Soggetto topico: Singular integrals; Calderón-Zygmund operator; Pseudodifferential operators; Noncommutative differential geometry; Lp spaces; Quantum theory; Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.); Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDE; Operator theory -- Integral, integro-differential, and pseudodifferential operators -- Pseudodifferential operators; Functional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Noncommutative measure and integration; Functional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- General theory of von Neumann algebras; Quantum theory -- Groups and algebras in quantum theory -- Noncommutative geometry
• Classificazione: 42B2042B3747G3046L5146L1081R60
• Altri autori: JungeMarius ParcetJavier
• Note generali: "July 2021. Volume 272."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Quantum Euclidean spaces -- Calderón-Zygmund Lp theory -- Pseudodifferential Lp calculus -- Lp regularity for elliptic PDEs.
• Sommario/riassunto: "We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes' pseudodifferential calculus for rotation algebras, thanks to a new form of Calderon-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce Lp-boundedness and Sobolev p-estimates for regular, exotic and forbidden symbols in the expected ranks. In the L2 level both Calderon-Vaillancourt and Bourdaud theorems for exotic and forbidden symbols are also generalized to the quantum setting. As a basic application of our methods, we prove Lp-regularity of solutions for elliptic PDEs"--
• Titolo autorizzato: Singular Integrals in Quantum Euclidean Spaces
• ISBN: 9781470467500; 147046750X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910975326203321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society