Titlebook: Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers; Cédric Arhancet,Christoph Kriegler Book 2022 The Editor(s

Analogy

Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers

Obligatory

Preliminaries,crossed product von Neumann algebras. Then we give useful results on Hilbertian valued noncommutative L.-spaces for the sequel of the book. Finally, we examine in detail the carré du champ and the first order differential calculus for semigroups of Fourier multipliers and semigroups of Schur multipliers.

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0075-8434 ded in the construction of its various non-commutative objecThis book on recent research in noncommutative harmonic analysis treats the L.p.?boundedness of Riesz transforms associated with Markovian semigroups of either Fourier?multipliers on non-abelian groups or Schur multipliers. The detailed stu

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Comprise

Introduction,s in various settings in that they have been studied in the literature. We also explain the emergence of noncommutative L.-spaces and noncommutative geometry in this context. Furthermore, we describe our main results concerning Riesz transforms, functional calculus of Hodge-Dirac operators and spect

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Preliminaries,tive L.-spaces and probabilities. In particular, the construction of our markovian semigroups of Fourier and Schur multipliers is a standing assumption in the rest of the book. We equally investigate vector-valued unbounded bilinear forms on Banach spaces which will be used as a framework for (the d

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休息

Boundedness of ,, Functional Calculus of Hodge-Dirac Operators, a bounded H. functional calculus on a bisector. We also provide Hodge decompositions. We equally show a similar result for Hodge-Dirac operators associated with markovian semigroups of Schur multipliers. Particular attention is paid to the domain of the Hodge-Dirac operators and different choices a

commonsense

Locally Compact Quantum Metric Spaces and Spectral Triples, spaces to some Markov semigroups of Fourier multipliers satisfying additional conditions: an injectivity and a gap condition on the cocycle which represents the semigroup, and the finite dimensionality (with explicit control on .) of the cocycle Hilbert space. We show a similar result for semigroup

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Introduction,eometry in this context. Furthermore, we describe our main results concerning Riesz transforms, functional calculus of Hodge-Dirac operators and spectral triples. We equally present examples that can used with our results and end with an overview of the contents of the other chapters.