Singular integrals in quantum Euclidean spaces

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 Calder...

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Bibliographic Details
Main Authors: González-Pérez, Adrían Manuel, Junge, Marius, Parcet, Javier
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2021
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Calderón-Zygmund operator
Calderón-Zygmund operator
Functional analysis > Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) > General theory of von Neumann algebras. msc
Functional analysis > Selfadjoint operator algebras ($C$-algebras, von Neumann ($W$-) algebras, etc.) > Noncommutative measure and integration. msc
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables > Harmonic analysis and PDE. msc
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables > Singular and oscillatory integrals (Calderón-Zygmund, etc.). msc
Lp spaces
Noncommutative differential geometry
Operator theory > Integral, integro-differential, and pseudodifferential operators > Pseudodifferential operators. msc
Pseudodifferential operators
Quantum theory
Quantum theory > Groups and algebras in quantum theory > Noncommutative geometry. msc
Singular integrals
pseudodifferential operator
Singular integral
quantum Euclidean space
ISBN:9781470449377, 1470449374
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary: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 Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution kernels. We deduce
Bibliography:Includes bibliographical references (p. 87-90)
July 2021, volume 272, number 1334 (fourth of 7 numbers)
ISBN:9781470449377
1470449374
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1334