An Inverse Spectral Theorem
Spectral Theory
2010-10-04 v1 Mathematical Physics
math.MP
Abstract
We prove a substantial extension of an inverse spectral theorem of Ambarzumyan, and show that it can be applied to arbitrary compact Riemannian manifolds, compact quantum graphs and finite combinatorial graphs, subject to the imposition of Neumann (or Kirchhoff) boundary conditions.
Cite
@article{arxiv.1010.0094,
title = {An Inverse Spectral Theorem},
author = {E. B. Davies},
journal= {arXiv preprint arXiv:1010.0094},
year = {2010}
}
Comments
15 pages. Keywords: inverse problems, Ambarzumyan, spectral geometry, heat kernel, heat trace asymptotics, quantum graph