| Description |
1 online resource (x, 193 pages) |
| Series |
Annals of mathematics studies ; number 188 |
|
Annals of mathematics studies ; no. 188.
|
| Contents |
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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 185-189) and index |
| Notes |
In English |
|
Print version record |
| Subject |
Laplacian operator.
|
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Eigenfunctions.
|
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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MATHEMATICS -- Differential Equations -- Partial.
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Eigenfunctions
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Laplacian operator
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| Form |
Electronic book
|
| ISBN |
9781400850549 |
|
1400850541 |
|
9781306375061 |
|
1306375061 |
|
