Journal of Geometric Analysis

, Volume 20, Issue 2, pp 439–471

Linear Representations and Isospectrality with Boundary Conditions

Authors

    • Institute of MathematicsHebrew University
  • Ram Band
    • Department of Physics of Complex SystemsThe Weizmann Institute of Science
Article

DOI: 10.1007/s12220-009-9115-6

Cite this article as:
Parzanchevski, O. & Band, R. J Geom Anal (2010) 20: 439. doi:10.1007/s12220-009-9115-6

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

IsospectralitySymmetryHear the shape of a drumLinear representationsBoundary value problemQuantum graphs

Mathematics Subject Classification (2000)

58J5358J3258D19

Copyright information

© Mathematica Josephina, Inc. 2009