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Hangzhou Lectures on Eigenfunctions of the Laplacian
Af: Christopher D. Sogge
Engelsk
Bogcover for Hangzhou Lectures on Eigenfunctions of the Laplacian af Christopher D. Sogge, 9780691160788
Specifikationer
Sprog:
Engelsk
Sider:
208
ISBN-13:
9780691160788
Indbinding:
Paperback
ISBN-10:
0691160783
Kategori:
Udg. Dato:
10 mar 2014
Størrelse i cm:
25,2 x 17,8 x 1,4
Forlag:
Serie:
Oplagsdato:
10 mar 2014
Forfatter(e):
Genre:

Hangzhou Lectures on Eigenfunctions of the Laplacian

Af: Christopher D. Sogge
Engelsk
Paperback 2014
Format:
Paperback
Bog beskrivelse

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.

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Specifikationer
Sprog:
Engelsk
Sider:
208
ISBN-13:
9780691160788
Indbinding:
Paperback
ISBN-10:
0691160783
Kategori:
Udg. Dato:
10 mar 2014
Størrelse i cm:
25,2 x 17,8 x 1,4
Forlag:
Serie:
Oplagsdato:
10 mar 2014
Forfatter(e):
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