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Product Code:  CONM/173 
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Book DetailsContemporary MathematicsVolume: 173; 1994; 299 ppMSC: Primary 58; 35; Secondary 05; 22; 53;
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 graphtheoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMSIMSSIAM 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.
ReadershipResearch mathematicians.

Table of Contents

Articles

Edoh Y. Amiran  An inverse problem and spectral invariants for billiards [ MR 1298194 ]

Jeff Angel, Steve Poulos, Audrey Terras, Cindy Trimble and Elinor Velasquez  Spherical functions and transforms on finite upper half planes: eigenvalues of the combinatorial Laplacian, uncertainty, traces [ MR 1298195 ]

Robert Brooks  $L^p$ spectral geometry [ MR 1298196 ]

Robert Brooks and Paul Glezen  An $L^p$ spectral bootstrap theorem [ MR 1298197 ]

Xianzhe Dai and Guofang Wei  Finite part of spectrum and isospectrality [ MR 1298198 ]

Jozef Dodziuk  Nonexistence of universal upper bounds for the first positive eigenvalue of the LaplaceBeltrami operator [ MR 1298199 ]

Koji Fujiwara  Convergence of the eigenvalues of Laplacians in a class of finite graphs [ MR 1298200 ]

Carolyn S. Gordon  Isospectral closed Riemannian manifolds which are not locally isometric. II [ MR 1298201 ]

Ruth Gornet  The length spectrum and representation theory on two and threestep nilpotent Lie groups [ MR 1298202 ]

Eugene Gutkin  A few remarks on the billiard ball problem [ MR 1298203 ]

Lizhen Ji and Steven Zelditch  Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces [ MR 1298204 ]

Yaroslav Kurylev  Inverse boundary problems on Riemannian manifolds [ MR 1298205 ]

Leonid Malozemov  Spectral theory of the differential Laplacian on the modified Koch curve [ MR 1298206 ]

Yiping Mao  Conjugate geodesic flows in negatively curved manifolds [ MR 1298207 ]

Hubert Pesce  Variétés isospectrales et représentations de groupes [ MR 1298208 ]

Yiannis N. Petridis  On differences of eigenvalues for flat tori and hyperbolic surfaces [ MR 1298209 ]

Gregory Quenell  Combinatorics of free product graphs [ MR 1298210 ]

Toshikazu Sunada  A discrete analogue of periodic magnetic Schrödinger operators [ MR 1298211 ]


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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 graphtheoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMSIMSSIAM 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.
Research mathematicians.

Articles

Edoh Y. Amiran  An inverse problem and spectral invariants for billiards [ MR 1298194 ]

Jeff Angel, Steve Poulos, Audrey Terras, Cindy Trimble and Elinor Velasquez  Spherical functions and transforms on finite upper half planes: eigenvalues of the combinatorial Laplacian, uncertainty, traces [ MR 1298195 ]

Robert Brooks  $L^p$ spectral geometry [ MR 1298196 ]

Robert Brooks and Paul Glezen  An $L^p$ spectral bootstrap theorem [ MR 1298197 ]

Xianzhe Dai and Guofang Wei  Finite part of spectrum and isospectrality [ MR 1298198 ]

Jozef Dodziuk  Nonexistence of universal upper bounds for the first positive eigenvalue of the LaplaceBeltrami operator [ MR 1298199 ]

Koji Fujiwara  Convergence of the eigenvalues of Laplacians in a class of finite graphs [ MR 1298200 ]

Carolyn S. Gordon  Isospectral closed Riemannian manifolds which are not locally isometric. II [ MR 1298201 ]

Ruth Gornet  The length spectrum and representation theory on two and threestep nilpotent Lie groups [ MR 1298202 ]

Eugene Gutkin  A few remarks on the billiard ball problem [ MR 1298203 ]

Lizhen Ji and Steven Zelditch  Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces [ MR 1298204 ]

Yaroslav Kurylev  Inverse boundary problems on Riemannian manifolds [ MR 1298205 ]

Leonid Malozemov  Spectral theory of the differential Laplacian on the modified Koch curve [ MR 1298206 ]

Yiping Mao  Conjugate geodesic flows in negatively curved manifolds [ MR 1298207 ]

Hubert Pesce  Variétés isospectrales et représentations de groupes [ MR 1298208 ]

Yiannis N. Petridis  On differences of eigenvalues for flat tori and hyperbolic surfaces [ MR 1298209 ]

Gregory Quenell  Combinatorics of free product graphs [ MR 1298210 ]

Toshikazu Sunada  A discrete analogue of periodic magnetic Schrödinger operators [ MR 1298211 ]