Cargando…
Geometry of the Spectrum.
Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1994.
|
| Colección: | Contemporary Mathematics Ser.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; An inverse problem and spectral invariants for billiards; Spherical functions and transforms on finite upper half planes: Eigenvalues of the combinatorial Laplacian, uncertainty, traces; 1. Introduction.; 2. Finite Upper Half Planes Hq and Their Spherical Functions.; 3. Aspects of Spherical Fourier Analysis on Hq.; 3.1. The Uncertainty Principle for the Spherical Transform.; 3.2. Selberg's Trace Formula for the Spherical Transform.; LP spectral geometry; An LP spectral bootstrap theorem; Finite part of spectrum and isospectrality.
- Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operatorConvergence of the eigenvalues of Laplacians in a class of finite graphs; Isospectral closed Riemannian manifolds which are not locally isometric, Part II; The length spectrum and representation theory on two and three-step nilpotent Lie groups; A few remarks on the billiard ball problem; Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces; Inverse boundary problems on Riemannian manifolds; Spectral theory of the differential Laplacian on the modified Koch curve.
- Conjugate geodesic flows in negatively curved manifoldsVariétés isospectrales et représentations de groupes; On differences of eigenvalues for flat tori and hyperbolic surfaces; Combinatorics of free product graphs; A discrete analogue of periodic magnetic SchrÜdinger operators.