| 书目名称 | Principal Symbol Calculus on Contact Manifolds |
| 编辑 | Yuri Kordyukov,Fedor Sukochev,Dmitriy Zanin |
| 视频video | |
| 概述 | the first complete treatment of Connes’ trace theorem on contact manifolds.proves the equivariance of the principal symbol on Heisenberg groups.introduces a natural measure on sub-Riemannian manifolds |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | .This book develops a C*-algebraic approach to the notion of principal symbol on Heisenberg groups and, using the fact that contact manifolds are locally modeled by Heisenberg groups, on compact contact manifolds. Applying abstract theorems due to Lord, Sukochev, Zanin and McDonald, a principal symbol on the Heisenberg group is introduced as a homomorphism of C*-algebras. This leads to a version of Connes’ trace theorem for Heisenberg groups, followed by a proof of the equivariant behavior of the principal symbol under Heisenberg diffeomorphisms. Using this equivariance and the authors’ globalization theorem, techniques are developed which enable further extensions to arbitrary stratified Lie groups and, as a consequence, the notion of a principal symbol on compact contact manifolds is described via a patching process. Finally, the Connes trace formula on compact contact sub-Riemannian manifolds is established and a spectrally correct version of the sub-Riemannian volume is defined (different from Popp‘s measure)...The book is aimed at graduate students and researchers working in spectral theory, Heisenberg analysis, operator algebras and noncommutative geometry.. |
| 出版日期 | Book 2024 |
| 关键词 | Principal symbol; Contact manifold; Heisenberg group; Equivariance; Connes Trace Theorem |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-69926-9 |
| isbn_softcover | 978-3-031-69925-2 |
| isbn_ebook | 978-3-031-69926-9Series 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 |
发表于 2025-3-21 19:48:00
