000 | 02250cam a2200253 i 4500 | ||
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001 | 136618 | ||
003 | ISI Library, Kolkata | ||
005 | 20160310123335.0 | ||
008 | 130823s2014 nju b 001 0 eng | ||
020 | _a9780691160788 (pbk. : alk. paper) | ||
040 |
_aISI Library _beng |
||
082 | 0 | 4 |
_a515.3533 _223 _bSo682 |
100 | 1 | _aSogge, Christopher D. | |
245 | 1 | 0 |
_aHangzhou lectures on eigenfunctions of the Laplacian / _cChristopher D. Sogge. |
260 |
_aPrinceton : _bPrinceton University Press, _c2014. |
||
300 |
_ax, 193 p. ; _c26 cm. |
||
490 | 0 |
_aAnnals of mathematics studies ; _vno 188. |
|
504 | _aIncludes bibliographical references and index. | ||
505 | 0 | _a1. A review : the Laplacian and the d'Alembertian -- 2. Geodesics and the Hadamard paramatrix -- 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. | |
520 | _aThis 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 | _aLaplacian operator. | |
650 | 0 | _aEigenfunctions. | |
942 |
_2ddc _cBK |
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999 |
_c420197 _d420197 |