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Annals of Mathematics Studies Hangzhou Lectures on Eigenfunctions of the Laplacian, Book 188, (Paperback)
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- Annals of Mathematics Studies Hangzhou Lectures on Eigenfunctions of the Laplacian, Book 188, (Paperback)
- Author: Princeton University Press
- ISBN: 9780691160788
- Format: Paperback
- Publication Date: 2014-03-10
- Page Count: 208
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- Book formatPaperback
- Fiction/nonfictionNon-Fiction
- GenreTextbooks
- Publication dateMarch, 2014
- Pages208
- SubgenreMathematical Analysis
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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. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.- Annals of Mathematics Studies Hangzhou Lectures on Eigenfunctions of the Laplacian, Book 188, (Paperback)
- Author: Princeton University Press
- ISBN: 9780691160788
- Format: Paperback
- Publication Date: 2014-03-10
- Page Count: 208
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Book format
Paperback
Fiction/nonfiction
Non-Fiction
Genre
Textbooks
Publication date
March, 2014
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