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Journal of Operator Theory

Volume 69, Issue 1, Winter 2013  pp. 195-208.

An inverse spectral theorem

Authors E.B. Davies
Author institution: Department of Mathematics, King's College London, Strand, London, SE21 7BS, U.K.

Summary:  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.

Keywords:  inverse problems, Ambarzumyan, heat kernel, heat trace asymptotics, quantum graph

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