{"product_id":"9783030990107","title":"Lecture Notes in Mathematics","description":"\u003ch1\u003eLecture Notes in Mathematics\u003c\/h1\u003e \u003ch2\u003eArhancet, Cédric; Kriegler, Christoph\u003c\/h2\u003e \u003cp\u003eThis book on recent research in noncommutative harmonic analysis treats the L\u003ci\u003e\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e 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 L\u003ci\u003e\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. \u003c\/p\u003e\u003cp\u003e 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 L\u003ci\u003e\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these L\u003ci\u003e\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e operations can be formulated on L\u003ci\u003e\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background.\u003c\/p\u003e\u003cp\u003e 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 L\u003ci\u003e\u003csup\u003ep\u003c\/sup\u003e\u003c\/i\u003e spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2022-05-06\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783030990107\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-030-99011-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 280\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":44805980127372,"sku":"9783030990107","price":58.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783030990107.jpg?v=1775675804","url":"https:\/\/lateknightbooks.com\/products\/9783030990107","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}