Finite deficiency indices and uniform remainder in Weyl's law

Abstract

We give a proof that in settings where Von Neumann deficiency indices are finite the spectral counting functions of two different self-adjoint extensions of the same symmetric operator differ by a uniformly bounded term (see also Birman-Solomjak's 'Spectral Theory of Self-adjoint operators in Hilbert Space') >. We apply this result to quantum graphs, pseudo-laplacians and surfaces with conical singularities.

7 p., references added

References in corpus (6)

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• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
• The trace formula for quantum graphs with general self adjoint boundary conditions
• Localised eigenfunctions in Seba billiards
• Compact polyhedral surfaces of an arbitrary genus and determinants of Laplacians
• Vacuum energy, spectral determinant and heat kernel asymptotics of graph Laplacians with general vertex matching conditions