By Christopher D. Sogge
ISBN-10: 0691160759
ISBN-13: 9780691160757
ISBN-10: 0691160783
ISBN-13: 9780691160788
Based on lectures given at Zhejiang college in Hangzhou, China, and Johns Hopkins college, this e-book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge supplies an explanation of the pointy Weyl formulation for the distribution of eigenvalues of Laplace-Beltrami operators, in addition to a higher model of the Weyl formulation, the Duistermaat-Guillemin theorem lower than ordinary assumptions at the geodesic movement. Sogge indicates that there's quantum ergodicity of eigenfunctions if the geodesic stream is ergodic.
Sogge starts with a remedy of the Hadamard parametrix earlier than proving the 1st major consequence, the pointy Weyl formulation. He avoids using Tauberian estimates and as a substitute depends on sup-norm estimates for eigenfunctions. the writer additionally supplies a quick creation to the desk bound part and the fundamentals of the idea of pseudodifferential operators and microlocal research. those are used to turn out the Duistermaat-Guillemin theorem. Turning to the comparable subject of quantum ergodicity, Sogge demonstrates that if the long term geodesic circulation is uniformly allotted, so much eigenfunctions show an analogous habit, within the feel that their mass turns into equidistributed as their frequencies visit infinity.
Read or Download Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) (Annals of Mathematics Studies) PDF
Best differential equations books
The 1st modern textbook on usual differential equations (ODEs) to incorporate directions on MATLAB®, Mathematica®, and Maple™, A path in usual Differential Equations makes a speciality of purposes and techniques of analytical and numerical recommendations, emphasizing methods utilized in the common engineering, physics, or arithmetic student's box of analysis.
Fatou, Julia, Montel,: le grand prix des sciences by Michèle Audin PDF
Remark Fatou et Julia ont inventé ce que l’on appelle aujourd’hui les ensembles de Julia, avant, pendant et après l. a. première guerre mondiale? L’histoire est racontée, avec ses mathématiques, ses conflits, ses personnalités. Elle est traitée à partir de assets nouvelles, et avec rigueur. On pourra s’y initier à l’itération des fractions rationnelles et à los angeles dynamique complexe (ensembles de Julia, de Mandelbrot, ensembles-limites).
This publication supplies a entire advent to numerical tools and research of stochastic techniques, random fields and stochastic differential equations, and provides graduate scholars and researchers robust instruments for realizing uncertainty quantification for threat research. assurance contains conventional stochastic ODEs with white noise forcing, robust and susceptible approximation, and the multi-level Monte Carlo process.
Brownian Motion and its Applications to Mathematical by Krzysztof Burdzy PDF
Those lecture notes offer an advent to the functions of Brownian movement to research and extra quite often, connections among Brownian movement and research. Brownian movement is a well-suited version for quite a lot of actual random phenomena, from chaotic oscillations of microscopic items, corresponding to flower pollen in water, to inventory marketplace fluctuations.
Extra resources for Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) (Annals of Mathematics Studies)
Sample text
Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188) (Annals of Mathematics Studies) by Christopher D. Sogge
by William
4.0