04656nam 22008173 450 991097532620332120231110215743.09781470467500147046750X(CKB)4940000000616258(MiAaPQ)EBC6798071(Au-PeEL)EBL6798071(RPAM)22493604(PPN)259971316(OCoLC)1275392622(EXLCZ)99494000000061625820211214d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierSingular Integrals in Quantum Euclidean Spaces1st ed.Providence :American Mathematical Society,2021.©2021.1 online resource (110 pages)Memoirs of the American Mathematical Society ;v.272"July 2021. Volume 272."9781470449377 1470449374 Includes bibliographical references.Quantum Euclidean spaces -- Calderón-Zygmund Lp theory -- Pseudodifferential Lp calculus -- Lp regularity for elliptic PDEs."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"--Provided by publisher.Memoirs of the American Mathematical Society Singular integralsCalderón-Zygmund operatorPseudodifferential operatorsNoncommutative differential geometryLp spacesQuantum theoryHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Singular and oscillatory integrals (Calderón-Zygmund, etc.)mscHarmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Harmonic analysis and PDEmscOperator theory -- Integral, integro-differential, and pseudodifferential operators -- Pseudodifferential operatorsmscFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Noncommutative measure and integrationmscFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- General theory of von Neumann algebrasmscQuantum theory -- Groups and algebras in quantum theory -- Noncommutative geometrymscSingular 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.515/.72342B2042B3747G3046L5146L1081R60mscGonzález-Pérez Adrían M1799715Junge Marius1643539Parcet Javier1799716MiAaPQMiAaPQMiAaPQBOOK9910975326203321Singular Integrals in Quantum Euclidean Spaces4344110UNINA