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Pointwise convergence of noncommutative fourier series / Guixiang Hong, Simeng Wang, Xumin Wang

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 302, number 1520 (October 2024)Publisher: Providence : American Mathematical Society, October 2024Description: v, 86 SeitenISBN:
  • 9781470471866
Subject(s): Additional physical formats: Erscheint auch als: Pointwise convergence of noncommutative fourier series. Online-Ausgabe Providence : American Mathematical Society, 2024. 1 Online-Ressource (v, 86 Seiten)MSC: MSC: 46L52 | 46L51 | 43A55 | 46L67 | 47L25Summary: This paper is devoted to the study of pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as summation methods and mean convergence of the associated noncommutative Fourier series. Based on this framework, this paper studies the refined counterpart of pointwise convergence of these Fourier series. As a key ingredient, we develop a noncommutative bootstrap method and establish a general criterion of maximal inequalities for approximate identities of noncommutative Fourier multipliers. Based on this criterion, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions tending to 1 pointwise, so that the associated Fourier multipliers on noncommutative Lp-spaces satisfy the pointwise convergence for all p>1. In a similar fashion, we also obtain results for a large subclass of groups (as well as quantum groups) with the Haagerup property and the weak amenability. We also consider the analogues of Fejér and Bochner-Riesz means in the noncommutative setting. Our approach heavily relies on the noncommutative ergodic theory in conjunction with abstract constructions of Markov semigroups, inspired by quantum probability and geometric group theory. Finally, we also obtain as a byproduct the dimension free bounds of the noncommutative Hardy-Littlewood maximal inequalities associated with convex bodies.PPN: PPN: 1910924334
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-302.2024,1520 Nicht ausleihbar
Total holds: 0
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