| 書目名稱 | Riesz Transforms, Hodge-Dirac Operators and Functional Calculus for Multipliers | | 編輯 | Cédric Arhancet,Christoph Kriegler | | 視頻video | http://file.papertrans.cn/831/830337/830337.mp4 | | 概述 | Solves the Junge–Mei–Parcet problem concerning the H∞ calculus of Hodge–Dirac operators.Introduces in a self-contained way all materials needed in the construction of its various non-commutative objec | | 叢書名稱 | Lecture Notes in Mathematics | | 圖書封面 |  | | 描述 | This 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 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.p.?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 L.p.. In the works of?Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these L.p.?operations can be?formulated on L.p.?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 excitin | | 出版日期 | Book 2022 | | 關鍵詞 | Riesz Transforms; Functional Calculus; Fourier Multipliers; Schur Multipliers; Noncommutative Lp-spaces; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-99011-4 | | isbn_softcover | 978-3-030-99010-7 | | isbn_ebook | 978-3-030-99011-4Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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