Cargando…
Hangzhou lectures on eigenfunctions of the Laplacian /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2014.
|
| Colección: | Annals of mathematics studies ;
no. 188. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | JSTOR_ocn869281847 | ||
| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
| 006 | m o d | ||
| 007 | cr mn||||||||| | ||
| 008 | 140128s2014 nju ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e rda |e pn |c N$T |d YDXCP |d IDEBK |d EBLCP |d E7B |d JSTOR |d MHW |d OSU |d DEBSZ |d OCLCQ |d OCLCF |d UIU |d COCUF |d OCLCQ |d COO |d PIFAG |d OTZ |d ZCU |d MERUC |d OCLCQ |d LGG |d DEGRU |d DEBBG |d AZK |d U3W |d EZ9 |d OCLCQ |d UUM |d STF |d OCLCQ |d NRAMU |d ICG |d VTS |d OCLCQ |d INT |d VT2 |d OCLCQ |d WYU |d LVT |d TKN |d OCLCQ |d LEAUB |d DKC |d OCLCQ |d UKAHL |d OCLCQ |d SFB |d OCLCQ |d AUD |d HS0 |d LUN |d OCLCO |d UIU |d OCLCQ |d OCLCO | ||
| 066 | |c (S | ||
| 019 | |a 868964132 |a 909875899 |a 961555091 |a 979686260 |a 992852934 | ||
| 020 | |a 9781400850549 |q (electronic bk.) | ||
| 020 | |a 1400850541 |q (electronic bk.) | ||
| 020 | |a 9781306375061 |q (electronic bk.) | ||
| 020 | |a 1306375061 |q (electronic bk.) | ||
| 020 | |z 9780691160757 |q (hardcover ; |q alk. paper) | ||
| 020 | |z 0691160759 |q (hardcover ; |q alk. paper) | ||
| 020 | |z 9780691160788 |q (pbk. ; |q alk. paper) | ||
| 020 | |z 0691160783 |q (pbk. ; |q alk. paper) | ||
| 024 | 7 | |a 10.1515/9781400850549 |2 doi | |
| 029 | 1 | |a AU@ |b 000052749452 | |
| 029 | 1 | |a CHBIS |b 010480684 | |
| 029 | 1 | |a CHVBK |b 336938756 | |
| 029 | 1 | |a DEBBG |b BV042523173 | |
| 029 | 1 | |a DEBBG |b BV043038789 | |
| 029 | 1 | |a DEBBG |b BV044064778 | |
| 029 | 1 | |a DEBSZ |b 40367462X | |
| 029 | 1 | |a DEBSZ |b 429949200 | |
| 029 | 1 | |a DEBSZ |b 44555830X | |
| 029 | 1 | |a GBVCP |b 1003757391 | |
| 035 | |a (OCoLC)869281847 |z (OCoLC)868964132 |z (OCoLC)909875899 |z (OCoLC)961555091 |z (OCoLC)979686260 |z (OCoLC)992852934 | ||
| 037 | |a 568757 |b MIL | ||
| 037 | |a 22573/ctt4kdpz6 |b JSTOR | ||
| 050 | 4 | |a QA406 |b .S66 2014eb | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 072 | 7 | |a MAT007020 |2 bisacsh | |
| 072 | 7 | |a MAT034000 |2 bisacsh | |
| 072 | 7 | |a MAT007000 |2 bisacsh | |
| 072 | 7 | |a MAT027000 |2 bisacsh | |
| 082 | 0 | 4 | |a 515/.3533 |2 23 |
| 084 | |a SI 830 |2 rvk | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Sogge, Christopher D. |q (Christopher Donald), |d 1960- |e author. | |
| 245 | 1 | 0 | |a Hangzhou lectures on eigenfunctions of the Laplacian / |c Christopher D. Sogge. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2014. | |
| 264 | 4 | |c ©2014 | |
| 300 | |a 1 online resource (x, 193 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |b PDF | ||
| 347 | |a text file | ||
| 490 | 1 | |a Annals of mathematics studies ; |v number 188 | |
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references (pages 185-189) and index. | ||
| 505 | 0 | |a 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. | |
| 588 | 0 | |a Print version record. | |
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Laplacian operator. | |
| 650 | 0 | |a Eigenfunctions. | |
| 650 | 4 | |a Analysis. | |
| 650 | 4 | |a Eigenfunctions. | |
| 650 | 4 | |a Laplacian operator. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Mathematik. | |
| 650 | 6 | |a Laplacien. | |
| 650 | 6 | |a Fonctions propres. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x Partial. |2 bisacsh | |
| 650 | 7 | |a Eigenfunctions |2 fast | |
| 650 | 7 | |a Laplacian operator |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Sogge, Christopher D. (Christopher Donald), 1960- |t Hangzhou lectures on eigenfunctions of the Laplacian. |d Princeton, New Jersey : Princeton University Press, 2014 |z 9780691160757 |w (DLC) 2013030692 |w (OCoLC)857234298 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 188. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt5hhp2g |z Texto completo |
| 880 | 0 | |6 505-00/(S |a Cover -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 A review: The Laplacian and the d'Alembertian -- 1.1 The Laplacian -- 1.2 Fundamental solutions of the d'Alembertian -- 2 Geodesics and the Hadamard parametrix -- 2.1 Laplace-Beltrami operators -- 2.2 Some elliptic regularity estimates -- 2.3 Geodesics and normal coordinates-a brief review -- 2.4 The Hadamard parametrix -- 3 The sharp Weyl formula -- 3.1 Eigenfunction expansions -- 3.2 Sup-norm estimates for eigenfunctions and spectral clusters -- 3.3 Spectral asymptotics: The sharp Weyl formula -- 3.4 Sharpness: Spherical harmonics -- 3.5 Improved results: The torus -- 3.6 Further improvements: Manifolds with nonpositive curvature -- 4 Stationary phase and microlocal analysis -- 4.1 The method of stationary phase -- 4.2 Pseudodifferential operators -- 4.3 Propagation of singularities and Egorov's theorem -- 4.4 The Friedrichs quantization -- 5 Improved spectral asymptotics and periodic geodesics -- 5.1 Periodic geodesics and trace regularity -- 5.2 Trace estimates -- 5.3 The Duistermaat-Guillemin theorem -- 5.4 Geodesic loops and improved sup-norm estimates -- 6 Classical and quantum ergodicity -- 6.1 Classical ergodicity -- 6.2 Quantum ergodicity -- Appendix -- A.1 The Fourier transform and the spaces S(Rn) and S0(Rn) -- A.2 The spaces D′(Ω) and E′(Ω) -- A.3 Homogeneous distributions -- A.4 Pullbacks of distributions -- A.5 Convolution of distributions -- Notes -- Bibliography -- Index -- Symbol Glossary. | |
| 938 | |a YBP Library Services |b YANK |n 11607113 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis27392234 | ||
| 938 | |a EBSCOhost |b EBSC |n 663526 | ||
| 938 | |a ebrary |b EBRY |n ebr10829680 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1561564 | ||
| 938 | |a De Gruyter |b DEGR |n 9781400850549 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH26388232 | ||
| 994 | |a 92 |b IZTAP | ||