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Hangzhou lectures on eigenfunctions of the Laplacian /
Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an imp...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton :
Princeton University Press,
2014.
|
| Series: | Annals of mathematics studies ;
no. 188. |
| Subjects: | |
| Online Access: |
Full text (Wentworth users only) |
| Local Note: | ProQuest Ebook Central |
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| 100 | 1 | |a Sogge, Christopher D. |q (Christopher Donald), |d 1960- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJmHDCkvJfg8xgpcdxYkjC | |
| 245 | 1 | 0 | |a Hangzhou lectures on eigenfunctions of the Laplacian / |c Christopher D. Sogge. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2014. | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (x, 193 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 347 | |b PDF | ||
| 347 | |a text file | ||
| 490 | 1 | |a Annals of mathematics studies ; |v number 188 | |
| 504 | |a Includes bibliographical references (pages 185-189) and index. | ||
| 505 | 0 | |a A review : the Laplacian and the d'Alembertian -- Geodesics and the Hadamard paramatrix -- The sharp Weyl formula -- Stationary phase and microlocal analysis -- Improved spectral asymptotics and periodic geodesics -- Classical and quantum ergodicity -- Appendix. | |
| 520 | |a Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Laplacian operator. | |
| 650 | 0 | |a Eigenfunctions. | |
| 758 | |i has work: |a Hangzhou lectures on eigenfunctions of the Laplacian (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGH3DCrkKRGMVXKWHKJxDq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Sogge, Christopher D. (Christopher Donald), 1960- |t Hangzhou lectures on eigenfunctions of the Laplacian. |d Princeton, New Jersey : Princeton University Press, 2014 |z 9780691160757 |w (DLC) 2013030692 |w (OCoLC)857234298 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 188. | |
| 852 | |b Ebooks |h ProQuest | ||
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/wit/detail.action?docID=1561564 |z Full text (Wentworth users only) |t 0 |
| 880 | 0 | |6 505-00/(S |a Cover -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 A review: The Laplacian and the d'Alembertian -- 1.1 The Laplacian -- 1.2 Fundamental solutions of the d'Alembertian -- 2 Geodesics and the Hadamard parametrix -- 2.1 Laplace-Beltrami operators -- 2.2 Some elliptic regularity estimates -- 2.3 Geodesics and normal coordinates-a brief review -- 2.4 The Hadamard parametrix -- 3 The sharp Weyl formula -- 3.1 Eigenfunction expansions -- 3.2 Sup-norm estimates for eigenfunctions and spectral clusters -- 3.3 Spectral asymptotics: The sharp Weyl formula -- 3.4 Sharpness: Spherical harmonics -- 3.5 Improved results: The torus -- 3.6 Further improvements: Manifolds with nonpositive curvature -- 4 Stationary phase and microlocal analysis -- 4.1 The method of stationary phase -- 4.2 Pseudodifferential operators -- 4.3 Propagation of singularities and Egorov's theorem -- 4.4 The Friedrichs quantization -- 5 Improved spectral asymptotics and periodic geodesics -- 5.1 Periodic geodesics and trace regularity -- 5.2 Trace estimates -- 5.3 The Duistermaat-Guillemin theorem -- 5.4 Geodesic loops and improved sup-norm estimates -- 6 Classical and quantum ergodicity -- 6.1 Classical ergodicity -- 6.2 Quantum ergodicity -- Appendix -- A.1 The Fourier transform and the spaces S(Rn) and S0(Rn) -- A.2 The spaces D′(Ω) and E′(Ω) -- A.3 Homogeneous distributions -- A.4 Pullbacks of distributions -- A.5 Convolution of distributions -- Notes -- Bibliography -- Index -- Symbol Glossary. | |
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