Positive definite functions and spectral properties of the Schrödinger operator with point interactions

DOI10.1134/S0001434611070157zbMath1244.47040OpenAlexW1992740860MaRDI QIDQ764023

N. I. Goloshchapova, Mark M. Malamud, Viktor P. Zastavnyi

Publication date: 13 March 2012

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434611070157

zbMATH Keywords

Schrödinger operatorsspectrumselfadjoint operatorsWeyl functiondeficiency indexpoint interactionGreen's formularadial positive definite functions

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10) Positive definite functions in one variable harmonic analysis (42A82)

Related Items (8)

Formulas for the eigenvalues of the iterated Laplacian with singular potentials ⋮ On real resonances for three-dimensional Schrödinger operators with point interactions ⋮ To the theory of nonnegative point Hamiltonians on a plane and in the space ⋮ Laplace operator with \(\delta\)-like potentials ⋮ Remark on the eigenvalues of the \(m\)-Laplacian in a punctured domain ⋮ Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions ⋮ Resolvents of well-posed problems for finite-rank perturbations of the polyharmonic operator in a punctured domain ⋮ Spectral properties of the iterated Laplacian with a potential in a punctured domain

Cites Work

• On the unitary equivalence of absolutely continuous parts of self-adjoint extensions
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• The von Neumann problem for nonnegative symmetric operators
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