Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions

N. Goloshchapova; M. Malamud; V. Zastavnyi

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arXiv · 1701.06436

Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions

N. Goloshchapova·M. Malamud·V. Zastavnyi

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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 Schrödinger 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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BibTeX RIS

N. Goloshchapova, M. Malamud, V. Zastavnyi. 2017-01-23. Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions. https://arxiv.org/abs/1701.06436

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