**Contemporary Mathematics**

Volume: 173;
1994;
299 pp;
Softcover

MSC: Primary 58; 35;
Secondary 05; 22; 53

**Print ISBN: 978-0-8218-5185-2
Product Code: CONM/173**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-0-8218-7764-7
Product Code: CONM/173.E**

List Price: $74.00

AMS Member Price: $59.20

MAA Member Price: $66.60

# Geometry of the Spectrum

Share this page *Edited by *
*Robert Brooks; Carolyn Gordon; Peter Perry*

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 analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.

#### Readership

Research mathematicians.

# Table of Contents

## Geometry of the Spectrum

- Contents v6 free
- An inverse problem and spectral invariants for billiards 112 free
- Spherical functions and transforms on finite upper half planes: Eigenvalues of the combinatorial Laplacian, uncertainty, traces 1526
- LP spectral geometry 7182
- An LP spectral bootstrap theorem 89100
- Finite part of spectrum and isospectrality 99110
- Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator 109120
- Convergence of the eigenvalues of Laplacians in a class of finite graphs 115126
- Isospectral closed Riemannian manifolds which are not locally isometric, Part II 121132
- The length spectrum and representation theory on two and three-step nilpotent Lie groups 133144
- A few remarks on the billiard ball problem 157168
- Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces 167178
- Inverse boundary problems on Riemannian manifolds 181192
- Spectral theory of the differential Laplacian on the modified Koch curve 193204
- Conjugate geodesic flows in negatively curved manifolds 225236
- Variétés isospectrales et représentations de groupes 231242
- On differences of eigenvalues for flat tori and hyperbolic surfaces 241252
- Combinatorics of free product graphs 257268
- A discrete analogue of periodic magnetic Schrödinger operators 283294