Hypoelliptic Laplacian and Orbital Integrals (AM-177) / / Jean-Michel Bismut.
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 essential...
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| Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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| VerfasserIn: | |
| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2011] ©2011 |
| Year of Publication: | 2011 |
| Edition: | Course Book |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
177 |
| Online Access: | |
| Physical Description: | 1 online resource (344 p.) :; 2 line illus. |
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Table of Contents:
- Frontmatter
- Contents
- Acknowledgments
- Introduction
- Chapter One. Clifford and Heisenberg algebras
- Chapter Two. The hypoelliptic Laplacian on X = G/K
- Chapter Three. The displacement function and the return map
- Chapter Four. Elliptic and hypoelliptic orbital integrals
- Chapter Five. Evaluation of supertraces for a model operator
- Chapter Six. A formula for semisimple orbital integrals
- Chapter Seven. An application to local index theory
- Chapter Eight. The case where [k (γ) ; p0] = 0
- Chapter Nine. A proof of the main identity
- Chapter Ten. The action functional and the harmonic oscillator
- Chapter Eleven. The analysis of the hypoelliptic Laplacian
- Chapter Twelve. Rough estimates on the scalar heat kernel
- Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b
- Chapter Fourteen. The heat kernel qXb;t for bounded b
- Chapter Fifteen. The heat kernel qXb;t for b large
- Bibliography
- Subject Index
- Index of Notation