Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / / Christopher D. Sogge.
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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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2014] ©2014 |
Year of Publication: | 2014 |
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Sogge, Christopher D., author. aut http://id.loc.gov/vocabulary/relators/aut Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / Christopher D. Sogge. Course Book Princeton, NJ : Princeton University Press, [2014] ©2014 1 online resource (208 p.) : 1 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 188 Frontmatter -- Contents -- Preface -- 1. A review: The Laplacian and the d'Alembertian -- 2. Geodesics and the Hadamard parametrix -- 3. The sharp Weyl formula -- 4. Stationary phase and microlocal analysis -- 5. Improved spectral asymptotics and periodic geodesics -- 6. Classical and quantum ergodicity -- Appendix -- Notes -- Bibliography -- Index -- Symbol Glossary restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Eigenfunctions. Laplacian operator. MATHEMATICS / Mathematical Analysis. bisacsh Duistermaat-Guillemin theorem. Egorov's theorem. Euclidean Laplacian. Euclidean space. Friedrichs quantization. Hadamard parametrix. LaplaceЂeltrami operators. Laplacian. Minkowski space. Riemannian manifolds. Weyl formula. classical ergodicity. compact manifolds. d'Alembertian. eigenfunctions. eigenvalues. elliptic regularity estimates. ergodic theory. geodesic flow. geodesics. high frequency eigenfunctions. invariant measure. limit theorems. manifolds. microlocal analysis. nonpositive curvature. normal coordinates. periodic geodesics. pseudodifferential operators. quantum chaos. quantum ergodicity. sharp Weyl formula. shrinking spectral bands. singularities. spectral asymptotics. spherical harmonics. stationary phase. sup-norm estimates. torus. trace estimates. wave equations. wave front sets. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691160757 https://doi.org/10.1515/9781400850549 https://www.degruyter.com/isbn/9781400850549 Cover https://www.degruyter.com/document/cover/isbn/9781400850549/original |
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Sogge, Christopher D., Sogge, Christopher D., |
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Sogge, Christopher D., Sogge, Christopher D., Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Preface -- 1. A review: The Laplacian and the d'Alembertian -- 2. Geodesics and the Hadamard parametrix -- 3. The sharp Weyl formula -- 4. Stationary phase and microlocal analysis -- 5. Improved spectral asymptotics and periodic geodesics -- 6. Classical and quantum ergodicity -- Appendix -- Notes -- Bibliography -- Index -- Symbol Glossary |
author_facet |
Sogge, Christopher D., Sogge, Christopher D., |
author_variant |
c d s cd cds c d s cd cds |
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VerfasserIn VerfasserIn |
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Sogge, Christopher D., |
title |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / |
title_full |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / Christopher D. Sogge. |
title_fullStr |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / Christopher D. Sogge. |
title_full_unstemmed |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / Christopher D. Sogge. |
title_auth |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / |
title_alt |
Frontmatter -- Contents -- Preface -- 1. A review: The Laplacian and the d'Alembertian -- 2. Geodesics and the Hadamard parametrix -- 3. The sharp Weyl formula -- 4. Stationary phase and microlocal analysis -- 5. Improved spectral asymptotics and periodic geodesics -- 6. Classical and quantum ergodicity -- Appendix -- Notes -- Bibliography -- Index -- Symbol Glossary |
title_new |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / |
title_sort |
hangzhou lectures on eigenfunctions of the laplacian (am-188) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2014 |
physical |
1 online resource (208 p.) : 1 line illus. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- 1. A review: The Laplacian and the d'Alembertian -- 2. Geodesics and the Hadamard parametrix -- 3. The sharp Weyl formula -- 4. Stationary phase and microlocal analysis -- 5. Improved spectral asymptotics and periodic geodesics -- 6. Classical and quantum ergodicity -- Appendix -- Notes -- Bibliography -- Index -- Symbol Glossary |
isbn |
9781400850549 9783110494914 9783110665925 9780691160757 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA406 |
callnumber-sort |
QA 3406 S66 42017 |
url |
https://doi.org/10.1515/9781400850549 https://www.degruyter.com/isbn/9781400850549 https://www.degruyter.com/document/cover/isbn/9781400850549/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.3533 |
dewey-sort |
3515.3533 |
dewey-raw |
515.3533 |
dewey-search |
515.3533 |
doi_str_mv |
10.1515/9781400850549 |
oclc_num |
869281847 |
work_keys_str_mv |
AT soggechristopherd hangzhoulecturesoneigenfunctionsofthelaplacianam188 |
status_str |
n |
ids_txt_mv |
(DE-B1597)447603 (OCoLC)869281847 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 |
is_hierarchy_title |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) / |
container_title |
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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