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1. |
Record Nr. |
UNINA9910464875403321 |
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Autore |
Sogge Christopher D |
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Titolo |
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) [[electronic resource]] |
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Pubbl/distr/stampa |
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Princeton, : Princeton University Press, 2014 |
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Descrizione fisica |
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1 online resource (206 p.) |
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Collana |
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Annals of Mathematics Studies |
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Disciplina |
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Soggetti |
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Eigenfunctions |
Laplacian operator |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di contenuto |
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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 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 |
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Sommario/riassunto |
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Based on lectures given at Zhejiang University in Hangzhou, China, and |
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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 |
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2. |
Record Nr. |
UNISA996389450103316 |
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Autore |
Bonaventure, Saint, Cardinal, <approximately 1217-1274.> |
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Titolo |
Here foloweth .ii. opuscules or smale werkes of saynt Bonaue[n]ture [[electronic resource] ] : moche necessarye, and profytable vnto all Chrystyanes specyally vnto relygious [per]sones put in to Englyshe by a brother of Syon Rycharde Whytforde |
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Pubbl/distr/stampa |
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Imprynted in the famous cytye of London, : By Rycharde Fawkes dwellynge in Duram rent or els in Paulles Churche yerde at the sygne of the A B C, [1530?] |
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Descrizione fisica |
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Soggetti |
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Acrostics |
Christian life |
Conduct of life |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Imprint from undated colphon. |
The attribution to Saint Bonaventura is open to doubt. Cf. ESTC. |
With printer's device on B4v: Richard Fakes. |
Date of publication suggested by STC (2nd ed.). |
Reproduction of original in: British Library. |
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