Autore	Hejhal Dennis A.
Pubbl/distr/stampa	Providence, Rhode Island, United States : , : American Mathematical Society, , 1992
Descrizione fisica	1 online resource (177 p.)
Disciplina	512/.7
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Selberg trace formula Automorphic functions Eigenvalues Laplacian operator
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0895-3
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Table of Contents""; ""0. Foreword""; ""I. Eigenvalues of the Laplacian for Hecke Triangle Groups""; ""1. Introduction and preliminary remarks""; ""2. The procedure in a nutshell""; ""3. Some theoretical difficulties""; ""4. Coefficient relations for N = 4 and 6""; ""5. ""Odd"" eigenvalues for N = 4, 5, 6, 7""; ""6. ""Even"" eigenvalues for N = 4, 5, 6, 7""; ""7. Some examples""; ""8. Some remarks about pseudo cusp forms""; ""9. Concluding remarks""; ""References""; ""Appendix A""; ""II. (Reprint of) Eigenvalues of the Laplacian for PSL(2,Z): Some New Results and Computational Techniques"" ""1. Introduction""""2. The basic procedure""; ""3. Some informal remarks concerning implementation of the basic procedure""; ""4. Further remarks""; ""5. The even eigenvalues less than 50""; ""6. The odd eigenvalues less than 50""; ""7. Even eigenvalues around R = 125""; ""8. Even eigenvalues around R = 250""; ""9. Even eigenvalues around R = 500""; ""10. Gaining greater accuracy""; ""11. Concluding remarks""; ""References""; ""Appendix B""
Record Nr.	UNINA-9910480745103321

Autore	Valdinoci Enrico <1974->
Pubbl/distr/stampa	Providence, Rhode Island : , : American Mathematical Society, , [2006]
Descrizione fisica	1 online resource (158 p.)
Disciplina	510 s 515/.39
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Geometry, Differential Laplacian operator Level set methods
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0462-1
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Modifications of the potential and of one-dimensional solutions""; ""Chapter 3. Geometry of the touching points""; ""Chapter 4. Measure theoretic results""; ""Chapter 5. Estimates on the measure of the projection of the contact set""; ""Chapter 6. Proof of Theorem 1.1""; ""Chapter 7. Proof of Theorem 1.2""; ""Chapter 8. Proof of Theorem 1.3""; ""Chapter 9. Proof of Theorem 1.4""; ""Appendix A. Proof of the measure theoretic results""; ""A.1. Proof of Lemma 4.1""; ""A.2. Proof of Lemma 4.2""; ""A.3. Proof of Lemma 4.3"" ""Appendix B. Summary of elementary lemmata""""Bibliography""
Record Nr.	UNINA-9910481007103321

Autore	Sogge Christopher D
Pubbl/distr/stampa	Princeton, : Princeton University Press, 2014
Descrizione fisica	1 online resource (206 p.)
Disciplina	515 515.3533 515/.3533
Collana	Annals of Mathematics Studies
Soggetto topico	Eigenfunctions Laplacian operator
Soggetto genere / forma	Electronic books.
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	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
Record Nr.	UNINA-9910464875403321

Autore	Bismut Jean-Michel
Edizione	[Course Book]
Pubbl/distr/stampa	Princeton, : Princeton University Press, 2011
Descrizione fisica	1 online resource (320 p.)
Disciplina	515.7242
Collana	Annals of mathematics studies
Soggetto topico	Differential equations, Hypoelliptic Laplacian operator Definite integrals Orbit method
Soggetto genere / forma	Electronic books.
Soggetto non controllato	Bianchi identity Brownian motion Casimir operator Clifford algebras Clifford variables Dirac operator Euclidean vector space Feynman-Kac formula Gaussian integral Gaussian type estimates Heisenberg algebras Kostant Leftschetz formula Littlewood-Paley decomposition Malliavin calculus Pontryagin maximum principle Selberg's trace formula Sobolev spaces Toponogov's theorem Witten complex action functional complexification conjugations convergence convexity de Rham complex displacement function distance function elliptic Laplacian elliptic orbital integrals fixed point formulas flat bundle general kernels general orbital integrals geodesic flow geodesics harmonic oscillator heat kernel heat kernels heat operators hypoelliptic Laplacian hypoelliptic deformation hypoelliptic heat kernel hypoelliptic heat kernels hypoelliptic operators hypoelliptic orbital integrals index formulas index theory infinite dimensional orbital integrals keat kernels local index theory locally symmetric space matrix part model operator nondegeneracy orbifolds orbital integrals parallel transport trivialization probabilistic construction pseudodistances quantitative estimates quartic term real vector space refined estimates rescaled heat kernel resolvents return map rough estimates scalar heat kernel scalar heat kernels scalar hypoelliptic Laplacian scalar hypoelliptic heat kernels scalar hypoelliptic operator scalar part semisimple orbital integrals smooth kernels standard elliptic heat kernel supertraces symmetric space symplectic vector space trace formula unbounded operators uniform bounds uniform estimates variational problems vector bundles wave equation wave kernel wave operator
ISBN	1-283-16387-X 9786613163875 1-4008-4057-0
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Frontmatter -- Contents -- Acknowledgments -- Introduction -- Chapter One. Clifford and Heisenberg algebras -- Chapter Two. The hypoelliptic Laplacian on X = G/K -- Chapter Three. The displacement function and the return map -- Chapter Four. Elliptic and hypoelliptic orbital integrals -- Chapter Five. Evaluation of supertraces for a model operator -- Chapter Six. A formula for semisimple orbital integrals -- Chapter Seven. An application to local index theory -- Chapter Eight. The case where [k (γ) ; p0] = 0 -- Chapter Nine. A proof of the main identity -- Chapter Ten. The action functional and the harmonic oscillator -- Chapter Eleven. The analysis of the hypoelliptic Laplacian -- Chapter Twelve. Rough estimates on the scalar heat kernel -- Chapter Thirteen. Refined estimates on the scalar heat kernel for bounded b -- Chapter Fourteen. The heat kernel qXb;t for bounded b -- Chapter Fifteen. The heat kernel qXb;t for b large -- Bibliography -- Subject Index -- Index of Notation
Record Nr.	UNINA-9910456831103321