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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
Peter Perry University of Kentucky, Lexington, KY
Front Cover for Geometry of the Spectrum
Available Formats:
Softcover ISBN: 978-0-8218-5185-2
Product Code: CONM/173
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
Electronic ISBN: 978-0-8218-7764-7
Product Code: CONM/173.E
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $59.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $118.50
MAA Member Price: $106.65
AMS Member Price: $94.80
Front Cover for Geometry of the Spectrum
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  • Front Cover for Geometry of the Spectrum
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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
Peter Perry University of Kentucky, Lexington, KY
Available Formats:
Softcover ISBN:  978-0-8218-5185-2
Product Code:  CONM/173
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
Electronic ISBN:  978-0-8218-7764-7
Product Code:  CONM/173.E
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $59.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $118.50
MAA Member Price: $106.65
AMS Member Price: $94.80
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1731994; 299 pp
    MSC: 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 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
     
     
    • 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 Laplace-Beltrami 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 three-step 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 ]
  • Request Review Copy
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Volume: 1731994; 299 pp
MSC: 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 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.

  • 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 Laplace-Beltrami 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 three-step 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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