Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers / / by Cédric Arhancet, Christoph Kriegler

• Autore: Arhancet Cédric
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022
• Edizione: 1st ed. 2022.
• Descrizione fisica: 1 online resource (288 pages)
• Disciplina: 515.7
• Soggetto topico: Operator theory; Functional analysis; Global analysis (Mathematics); Manifolds (Mathematics); Operator Theory; Functional Analysis; Global Analysis and Analysis on Manifolds
• Persona (resp. second.): KrieglerChristoph
• Nota di bibliografia: Includes bibliographical references (pages 265-274) and index.
• Nota di contenuto: Intro -- Preface -- Acknowledgements -- Contents -- 1 Introduction -- 2 Preliminaries -- 2.1 Operators, Functional Calculus and Semigroups -- 2.2 q-Gaussian Functors, Isonormal Processes and Probability -- 2.3 Vector-Valued Unbounded Bilinear Forms on Banach Spaces -- 2.4 Transference of Fourier Multipliers on Crossed Product Von Neumann Algebras -- 2.5 Hilbertian Valued Noncommutative Lp-Spaces -- 2.6 Carré Du Champ and First Order Differential Calculus for Fourier Multipliers -- 2.7 Carré Du Champ and First Order Differential Calculus for Schur Multipliers -- 3 Riesz Transforms Associated to Semigroups of Markov Multipliers -- 3.1 Khintchine Inequalities for q-Gaussians in Crossed Products -- 3.2 Lp-Kato's Square Root Problem for Semigroups of Fourier Multipliers -- 3.3 Extension of the Carré du Champ for Fourier Multipliers -- 3.4 Lp-Kato's Square Root Problem for Semigroups of Schur Multipliers -- 3.5 Meyer's Problem for Semigroups of Schur Multipliers -- 4 Boundedness of H∞ Functional Calculusof Hodge-Dirac Operators -- 4.1 Boundedness of Functional Calculus of Hodge-Dirac Operators for Fourier Multipliers -- 4.2 Extension to Full Hodge-Dirac Operator and Hodge Decomposition -- 4.3 Hodge-Dirac Operator on Lp(VN(G)) Ωψ,q,p -- 4.4 Bimodule Ωψ,q,p,c -- 4.5 Hodge-Dirac Operators Associated to Semigroups of Markov Schur Multipliers -- 4.6 Extension to Full Hodge-Dirac Operator and Hodge Decomposition -- 4.7 Independence from H and α -- 5 Locally Compact Quantum Metric Spaces and Spectral Triples -- 5.1 Background on Quantum Locally Compact Metric Spaces -- 5.2 Quantum Compact Metric Spaces Associated to Semigroups of Fourier Multipliers -- 5.3 Gaps and Estimates of Norms of Schur Multipliers -- 5.4 Seminorms Associated to Semigroups of Schur Multipliers -- 5.5 Quantum Metric Spaces Associated to Semigroups of Schur Multipliers. ; 5.6 Gaps of Some Markovian Semigroups of Schur and Fourier Multipliers -- 5.7 Banach Spectral Triples -- 5.8 Spectral Triples Associated to Semigroupsof Fourier Multipliers I -- 5.9 Spectral Triples Associated to Semigroupsof Fourier Multipliers II -- 5.10 Spectral Triples Associated to Semigroupsof Schur Multipliers I -- 5.11 Spectral Triples Associated to Semigroupsof Schur Multipliers II -- 5.12 Bisectoriality and Functional Calculus of the Dirac Operator II -- A Appendix: Lévy Measures and 1-Cohomology -- References -- Index.
• Sommario/riassunto: This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.
• Titolo autorizzato: Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers
• ISBN: 3-030-99011-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910568280303321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 1617-9692 ; ; 2304