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MARC 21

Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers
Tag	Description
020	$a9783030990114
082	$a515.724
099	$aOnline resource: Springer
100	$aArhancet, Cédric
245	$aRiesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers$h[EBook]$cCédric Arhancet, Christoph Kriegler
260	$aCham$bSpringer International Publishing$c2022
300	$bonline resource (xii, 280 p.)
440	$aLecture notes in mathematics.$v2304
520	$aThis 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.
533	$aDigital reproduction.-$bCham :$cSpringer International Publishing,$d2022. -$nDigital book. Cham Springer Nature 2022. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
700	$aKriegler, Christoph
856	$uhttps://doi.org/10.1007/978-3-030-99011-4