Hypoelliptic Laplacian and orbital integrals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2011]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 177 |
| Schlagworte: | |
| Online-Zugang: | URL des Erstveröffentlichers Volltext |
| Beschreibung: | Main description: This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof |
| Beschreibung: | 1 Online-Ressource (344 S.) |
| ISBN: | 9781400840571 |
| DOI: | 10.1515/9781400840571 |
Internformat
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| 490 | 1 | |a Annals of Mathematics Studies |v number 177 | |
| 500 | |a Main description: This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof | ||
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Datensatz im Suchindex
| _version_ | 1804153276232368128 |
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| any_adam_object | |
| author | Bismut, Jean-Michel 1948- |
| author_GND | (DE-588)141840056 |
| author_facet | Bismut, Jean-Michel 1948- |
| author_role | aut |
| author_sort | Bismut, Jean-Michel 1948- |
| author_variant | j m b jmb |
| building | Verbundindex |
| bvnumber | BV042522928 |
| classification_rvk | SI 830 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)1165505354 (DE-599)BVBBV042522928 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400840571 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:02Z |
| institution | BVB |
| isbn | 9781400840571 |
| language | English |
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| spelling | Bismut, Jean-Michel 1948- (DE-588)141840056 aut Hypoelliptic Laplacian and orbital integrals Princeton, N.J. Princeton University Press [2011] © 2011 1 Online-Ressource (344 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 177 Main description: This book uses the hypoelliptic Laplacian to evaluate semisimple orbital integrals in a formalism that unifies index theory and the trace formula. The hypoelliptic Laplacian is a family of operators that is supposed to interpolate between the ordinary Laplacian and the geodesic flow. It is essentially the weighted sum of a harmonic oscillator along the fiber of the tangent bundle, and of the generator of the geodesic flow. In this book, semisimple orbital integrals associated with the heat kernel of the Casimir operator are shown to be invariant under a suitable hypoelliptic deformation, which is constructed using the Dirac operator of Kostant. Their explicit evaluation is obtained by localization on geodesics in the symmetric space, in a formula closely related to the Atiyah-Bott fixed point formulas. Orbital integrals associated with the wave kernel are also computed. Estimates on the hypoelliptic heat kernel play a key role in the proofs, and are obtained by combining analytic, geometric, and probabilistic techniques. Analytic techniques emphasize the wavelike aspects of the hypoelliptic heat kernel, while geometrical considerations are needed to obtain proper control of the hypoelliptic heat kernel, especially in the localization process near the geodesics. Probabilistic techniques are especially relevant, because underlying the hypoelliptic deformation is a deformation of dynamical systems on the symmetric space, which interpolates between Brownian motion and the geodesic flow. The Malliavin calculus is used at critical stages of the proof Orbitalintegral (DE-588)4317881-9 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 gnd rswk-swf Hypoelliptischer Operator (DE-588)4138891-4 gnd rswk-swf Hypoelliptischer Operator (DE-588)4138891-4 s Laplace-Operator (DE-588)4166772-4 s Orbitalintegral (DE-588)4317881-9 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-691-15129-8 Annals of Mathematics Studies number 177 (DE-604)BV040389493 177 https://doi.org/10.1515/9781400840571?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400840571&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bismut, Jean-Michel 1948- Hypoelliptic Laplacian and orbital integrals Annals of Mathematics Studies Orbitalintegral (DE-588)4317881-9 gnd Laplace-Operator (DE-588)4166772-4 gnd Hypoelliptischer Operator (DE-588)4138891-4 gnd |
| subject_GND | (DE-588)4317881-9 (DE-588)4166772-4 (DE-588)4138891-4 |
| title | Hypoelliptic Laplacian and orbital integrals |
| title_auth | Hypoelliptic Laplacian and orbital integrals |
| title_exact_search | Hypoelliptic Laplacian and orbital integrals |
| title_full | Hypoelliptic Laplacian and orbital integrals |
| title_fullStr | Hypoelliptic Laplacian and orbital integrals |
| title_full_unstemmed | Hypoelliptic Laplacian and orbital integrals |
| title_short | Hypoelliptic Laplacian and orbital integrals |
| title_sort | hypoelliptic laplacian and orbital integrals |
| topic | Orbitalintegral (DE-588)4317881-9 gnd Laplace-Operator (DE-588)4166772-4 gnd Hypoelliptischer Operator (DE-588)4138891-4 gnd |
| topic_facet | Orbitalintegral Laplace-Operator Hypoelliptischer Operator |
| url | https://doi.org/10.1515/9781400840571?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400840571&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT bismutjeanmichel hypoellipticlaplacianandorbitalintegrals |