LEADER 03051nam 22004453u 450 001 9910809752203321 005 20230803201645.0 035 $a(CKB)3710000000085963 035 $a(EBL)1561564 035 $a(OCoLC)869281847 035 $a(MiAaPQ)EBC1561564 035 $a(EXLCZ)993710000000085963 100 $a20140421d2014|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 200 10$aHangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)$b[electronic resource] 210 $aPrinceton $cPrinceton University Press$d2014 215 $a1 online resource (206 p.) 225 1 $aAnnals of Mathematics Studies 300 $aDescription based upon print version of record. 311 $a0-691-16078-3 327 $aCover; 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 327 $a3.5 Improved results: The torus3.6 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 330 $a Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. Sogge begins with a treatment of the Hadamard parametrix before proving the fi 410 0$aAnnals of Mathematics Studies 606 $aEigenfunctions 606 $aLaplacian operator 615 4$aEigenfunctions. 615 4$aLaplacian operator. 676 $a515 676 $a515.3533 676 $a515/.3533 700 $aSogge$b Christopher D$0524956 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9910809752203321 996 $aHangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)$93948010 997 $aUNINA