Journal of Geometric Analysis

, Volume 20, Issue 2, pp 439–471 | Cite as

Linear Representations and Isospectrality with Boundary Conditions

Article

Abstract

We present a method for constructing families of isospectral systems, using linear representations of finite groups. We focus on quantum graphs, for which we give a complete treatment. However, the method presented can be applied to other systems such as manifolds and two-dimensional drums. This is demonstrated by reproducing some known isospectral drums, and new examples are obtained as well. In particular, Sunada’s method (Ann. Math. 121, 169–186, 1985) is a special case of the one presented.

Keywords

Isospectrality Symmetry Hear the shape of a drum Linear representations Boundary value problem Quantum graphs 

Mathematics Subject Classification (2000)

58J53 58J32 58D19 

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Copyright information

© Mathematica Josephina, Inc. 2009

Authors and Affiliations

  1. 1.Institute of MathematicsHebrew UniversityJerusalemIsrael
  2. 2.Department of Physics of Complex SystemsThe Weizmann Institute of ScienceRehovotIsrael

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