Quasi-isospectrality on quantum graphs

Abstract

Consider two quantum graphs with the standard Laplace operator and non-Robin type boundary conditions at all vertices. We show that if their eigenvalue-spectra agree everywhere aside from a sufficiently sparse set, then the eigenvalue-spectra and the length-spectra of the two quantum graphs are identical, with the possible exception of the multiplicity of the eigenvalue zero. Similarly if their length-spectra agree everywhere aside from a sufficiently sparse set, then the quantum graphs have the same eigenvalue-spectrum and length-spectrum, again with the possible exception of the eigenvalue zero.

This article has now been published but unfortunately the published version contains an error in the treatment of the eigenvalue zero. The version here is the corrected version

References in corpus (3)

• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
• The trace formula for quantum graphs with general self adjoint boundary conditions
• Monotone unitary families