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Riesz transforms, Hodge-Dirac operat...

Arhancet, Cedric.

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Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers

Record Type:	Electronic resources : Monograph/item
Title/Author:	Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers/ by Cedric Arhancet, Christoph Kriegler.
Author:	Arhancet, Cedric.
other author:	Kriegler, Christoph.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	xii, 280 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Riesz spaces. -
Online resource:	https://doi.org/10.1007/978-3-030-99011-4
ISBN:	9783030990114

Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers
Arhancet, Cedric.

Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers[electronic resource] /by Cedric Arhancet, Christoph Kriegler. - Cham :Springer International Publishing :2022. - xii, 280 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23041617-9692 ;. - Lecture notes in mathematics ;v. 2304..

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.

ISBN: 9783030990114

Standard No.: 10.1007/978-3-030-99011-4doiSubjects--Topical Terms:

1640814
Riesz spaces.

LC Class. No.: QA322 / .A74 2022

Dewey Class. No.: 515.73

Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers
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490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2304
520 $a 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.
650 0 $a Riesz spaces. $3 1640814
650 0 $a Operator theory. $3 542531
650 0 $a Functional analysis. $3 531838
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650 1 4 $a Operator Theory. $3 897311
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
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