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Record Nr. |
UNINA9910975326203321 |
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Autore |
González-Pérez Adrían M |
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Titolo |
Singular Integrals in Quantum Euclidean Spaces |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2021 |
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©2021 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (110 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.272 |
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Classificazione |
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42B2042B3747G3046L5146L1081R60 |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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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 |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Quantum Euclidean spaces -- Calderón-Zygmund Lp theory -- Pseudodifferential Lp calculus -- Lp regularity for elliptic PDEs. |
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Sommario/riassunto |
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"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"-- |
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