Principal Symbol Calculus on Contact Manifolds
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 symbo...
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| Tác giả của công ty: | |
| Định dạng: | Điện tử eBook |
| Ngôn ngữ: | Tiếng Anh |
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Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
|
| Phiên bản: | 1st ed. 2024. |
| Loạt: | Lecture Notes in Mathematics,
2359 |
| Những chủ đề: | |
| Truy cập trực tuyến: | https://doi.org/10.1007/978-3-031-69926-9 |
| Các nhãn: |
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| 100 | 1 | |a Kordyukov, Yuri. |e author. |0 (orcid)0000-0003-2957-2873 |1 https://orcid.org/0000-0003-2957-2873 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Principal Symbol Calculus on Contact Manifolds |h [electronic resource] / |c by Yuri Kordyukov, Fedor Sukochev, Dmitriy Zanin. |
| 250 | |a 1st ed. 2024. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2024. | |
| 300 | |a 1 online resource (XIV, 156 p. 2 illus.). | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
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| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 2359 | |
| 505 | 0 | |a Preface -- Foreword by Nigel Higson -- Introduction -- Principal Symbol on the Heisenberg Group -- Equivariance of the Principal Symbol Under Heisenberg Diffeomorphisms -- Principal Symbol on Contact Manifolds -- Bibliography. | |
| 520 | |a 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. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
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| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Functional analysis. | |
| 650 | 0 | |a Operator theory. | |
| 650 | 1 | 4 | |a Functional Analysis. |
| 650 | 2 | 4 | |a Operator Theory. |
| 700 | 1 | |a Sukochev, Fedor. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Zanin, Dmitriy. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||