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.