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[null,"1.","Record Nr.",null,"UNINA9910789041203321"]
[null,null,"Autore",null,"Sogge Christopher D"]
[null,null,"Titolo",null,"Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) [[electronic resource]]"]
[null,null,"Pubbl/distr/stampa",null,"Princeton, : Princeton University Press, 2014"]
[null,null,"Descrizione fisica",null,"1 online resource (206 p.)"]
[null,null,"Collana",null,"Annals of Mathematics Studies"]
[null,null,"Disciplina",null,"515"]
[{"$nulls":4},"515.3533"]
[{"$nulls":4},"515/.3533"]
[null,null,"Soggetti",null,"Eigenfunctions"]
[{"$nulls":4},"Laplacian operator"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,"Nota di contenuto",null,"Cover; Title; Copyright; Dedication; Contents; Preface; 1 A review: The Laplacian and the d'Alembertian; 1.1 The Laplacian; 1.2 Fundamental solutions of the d'Alembertian; 2 Geodesics and the Hadamard parametrix; 2.1 Laplace-Beltrami operators; 2.2 Some elliptic regularity estimates; 2.3 Geodesics and normal coordinates-a brief review; 2.4 The Hadamard parametrix; 3 The sharp Weyl formula; 3.1 Eigenfunction expansions; 3.2 Sup-norm estimates for eigenfunctions and spectral clusters; 3.3 Spectral asymptotics: The sharp Weyl formula; 3.4 Sharpness: Spherical harmonics"]
[{"$nulls":4},"3.5 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"]
[null,null,null,"Sommario/riassunto","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 "]
[{"$nulls":4},"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"]