MARC details
| 000 -LEADER |
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| fixed length control field |
02250cam a2200253 i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
136618 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20160310123335.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
130823s2014 nju b 001 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780691160788 (pbk. : alk. paper) |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| Language of cataloging |
eng |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
515.3533 |
| Edition number |
23 |
| Item number |
So682 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Sogge, Christopher D. |
| 245 10 - TITLE STATEMENT |
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| Title |
Hangzhou lectures on eigenfunctions of the Laplacian / |
| Statement of responsibility, etc |
Christopher D. Sogge. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Princeton : |
| Name of publisher, distributor, etc |
Princeton University Press, |
| Date of publication, distribution, etc |
2014. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
x, 193 p. ; |
| Dimensions |
26 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Annals of mathematics studies ; |
| Volume number/sequential designation |
no 188. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. A review : the Laplacian and the d'Alembertian --<br/>2. Geodesics and the Hadamard paramatrix --<br/>3. The sharp Weyl formula --<br/>4. Stationary phase and microlocal analysis --<br/>5. Improved spectral asymptotics and periodic geodesics --<br/>6. Classical and quantum ergodicity --<br/>Appendix --<br/>Notes --<br/>Bibliography --<br/>Index --<br/>Symbol glossary. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Laplacian operator. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Eigenfunctions. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
