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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. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an imp...
| Autor principal: | |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2014.
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 008 | 140128s2014 nju o 00 0 eng d | ||
| 020 | |a 9781400850549 | ||
| 020 | |z 9780691160757 | ||
| 020 | |z 9780691160788 | ||
| 040 | |a MdBmJHUP |c MdBmJHUP | ||
| 100 | 1 | |a Sogge, Christopher D. |q (Christopher Donald), |d 1960- |e author. | |
| 245 | 1 | 0 | |a Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / |c Christopher D. Sogge. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2014. | |
| 264 | 3 | |a Baltimore, Md. : |b Project MUSE, |c 0000 | |
| 264 | 4 | |c ©2014. | |
| 300 | |a 1 online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 0 | |a Annals of mathematics studies ; |v number 188 | |
| 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 | |a Description based on print version record. | ||
| 650 | 7 | |a Laplacian operator. |2 fast |0 (OCoLC)fst00992600 | |
| 650 | 7 | |a Eigenfunctions. |2 fast |0 (OCoLC)fst00904026 | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 6 | |a Fonctions propres. | |
| 650 | 6 | |a Laplacien. | |
| 650 | 4 | |a Mathematik. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Laplacian operator. | |
| 650 | 4 | |a Eigenfunctions. | |
| 650 | 4 | |a Analysis. | |
| 650 | 0 | |a Eigenfunctions. | |
| 650 | 0 | |a Laplacian operator. | |
| 655 | 7 | |a Electronic books. |2 local | |
| 710 | 2 | |a Project Muse. |e distributor | |
| 830 | 0 | |a Book collections on Project MUSE. | |
| 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. | |
| 856 | 4 | 0 | |z Texto completo |u https://projectmuse.uam.elogim.com/book/30745/ |
| 945 | |a Project MUSE - Custom Collection | ||