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Geometry of the Spectrum
Edited by: Robert Brooks, University of Southern California, Los Angeles, CA, Carolyn Gordon, Dartmouth College, Hanover, NH, and Peter Perry, University of Kentucky, Lexington, KY
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Contemporary Mathematics
1994; 299 pp; softcover
Volume: 173
ISBN-10: 0-8218-5185-3
ISBN-13: 978-0-8218-5185-2
List Price: US$70 Member Price: US$56
Order Code: CONM/173

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.

Research mathematicians.

• E. Y. Amiran -- An inverse problem and spectral invariants for billards
• J. Angel, S. Poulos, A. Terras, C. Trimble, and E. Velasquez -- Spherical functions and transforms on finite upper half planes: Eigenvalues of the combinatorial Laplacian, uncertainty, traces
• R. Brooks -- $$L^p$$ spectral geometry
• R. Brooks and P. Glezen -- An $$L^p$$ spectral bootstrap theorem
• X. Dai and G. Wei -- Finite part of spectrum and isospectrality
• J. Dodziuk -- Nonexistence of universal upper bounds for the first positive eigenvalue of the Laplace-Beltrami operator
• K. Fujiwara -- Convergence of the eigenvalues of Laplacians in a class of finite graphs
• C. S. Gordon -- Isospectral closed Riemannian manifolds which are not locally isometric, Part II
• R. Gornet -- The length spectrum and representation theory on two and three-step nilpotent Lie groups
• E. Gutkin -- A few remarks on the billiard ball problem
• L. Ji and S. Zelditch -- Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces
• Ya. Kurylev -- Inverse boundary problems on Riemannian manifolds
• L. Malozemov -- Spectral theory of the differential Laplacian on the modified Koch curve
• Y. Mao -- Conjugate geodesic flows in negatively curved manifolds
• H. Pesce -- Variétés isospectrales et représentations de groupes
• Y. N. Petridis -- On differences of eigenvalues for flat tori and hyperbolic surfaces
• G. Quenell -- Combinatorics of free product graphs
• T. Sunada -- A discrete analogue of periodic magnetic Schrödinger operators