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Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions (1701.06436v1)
Published 23 Jan 2017 in math.SP
Abstract: We complete the classical Schoenberg representation theorem for radial positive definite functions. We apply this result to study spectral properties of self-adjoint realizations of two- and three-dimensional Schr\"odinger operators with point interactions on a finite set. In particular, we prove that any realization has purely absolutely continuous non-negative spectrum.
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