Hangzhou lectures on eigenfunctions of the Laplacian (Book, 2014) [WorldCat.org]
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Hangzhou lectures on eigenfunctions of the Laplacian

Hangzhou lectures on eigenfunctions of the Laplacian

Author: Christopher D Sogge
Publisher: Princeton : Princeton University Press, 2014.
Series: Annals of mathematics studies, 188.
Edition/Format:   Print book : EnglishView all editions and formats
Publication:Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. It shows that there is quantum ergodicity  Read more...


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Document Type: Book
All Authors / Contributors: Christopher D Sogge
ISBN: 9780691160757 0691160759 9780691160788 0691160783
OCLC Number: 879604506
In: Sogge, Christopher D
Description: x, 193 Seiten ; 24 cm.
Contents: Preface ix 1A review: The Laplacian and the d'Alembertian 1 1.1 The Laplacian 1 1.2 Fundamental solutions of the d'Alembertian 6 2Geodesics and the Hadamard parametrix 16 2.1 Laplace-Beltrami operators 16 2.2 Some elliptic regularity estimates 20 2.3 Geodesics and normal coordinates|a brief review 24 2.4 The Hadamard parametrix 31 3The sharp Weyl formula 39 3.1 Eigenfunction expansions 39 3.2 Sup-norm estimates for eigenfunctions and spectral clusters 48 3.3 Spectral asymptotics: The sharp Weyl formula 53 3.4 Sharpness: Spherical harmonics 55 3.5 Improved results: The torus 58 3.6 Further improvements: Manifolds with nonpositive curvature 65 4Stationary phase and microlocal analysis 71 4.1 The method of stationary phase 71 4.2 Pseudodifferential operators 86 4.3 Propagation of singularities and Egorov's theorem 103 4.4 The Friedrichs quantization 111 5Improved spectral asymptotics and periodic geodesics 120 5.1 Periodic geodesics and trace regularity 120 5.2 Trace estimates 123 5.3 The Duistermaat-Guillemin theorem 132 5.4 Geodesic loops and improved sup-norm estimates 136 6Classical and quantum ergodicity 141 6.1 Classical ergodicity 141 6.2 Quantum ergodicity 153 Appendix 165 A.1 The Fourier transform and the spaces S( n) and S'( n)) 165 A.2 The spaces D'(OMEGA) and E'(OMEGA) 169 A.3 Homogeneous distributions 173 A.4 Pullbacks of distributions 176 A.5 Convolution of distributions 179 Notes 183 Bibliography 185 Index 191 Symbol Glossary 193
Series Title: Annals of mathematics studies, 188.
Responsibility: Christopher D. Sogge.


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"The book is very well written... I would definitely recommend it to anybody who wants to learn spectral geometry."--Leonid Friedlander, Mathematical Reviews

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