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

DOI10.1002/MANA.201100132zbMath1272.47005arXiv1701.06436OpenAlexW2074658856MaRDI QIDQ4648244

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

Publication date: 8 November 2012

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.06436

zbMATH Keywords

Schrödinger operatorspectrumpositive definite functionpoint interactionsself-adjoint extension

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (8)

On real resonances for three-dimensional Schrödinger operators with point interactions ⋮ Invariant Schrödinger operators with point interactions at the vertices of a regular polyhedron ⋮ Radial positive definite functions and Schoenberg matrices with negative eigenvalues ⋮ To the theory of nonnegative point Hamiltonians on a plane and in the space ⋮ Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definite functions ⋮ Schoenberg matrices of radial positive definite functions and Riesz sequences of translates in \(L^2(\mathbb R^n)\) ⋮ Strictly positive definite functions on the space of infinite diagonal matrices ⋮ A solution to the energy minimization problem constrained by a density function

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Cites Work

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• On the unitary equivalence of absolutely continuous parts of self-adjoint extensions
• Weyl function and spectral properties of self-adjoint extensions
• Positive definite functions and spectral properties of the Schrödinger operator with point interactions
• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• A new class of oscillatory radial basis functions
• Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrödinger operators revisited
• On symmetries in the theory of finite rank singular perturbations
• On Abel-Poisson type and Riesz means
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• The von Neumann problem for nonnegative symmetric operators
• Elliptic operators with boundary conditions on a subset of measure zero
• Monotone Funktionen, Stieltjessche Integrale und harmonische Analyse
• The extension theory of Hermitian operators and the moment problem
• A Criterion for a Characteristic Function and a Polyá-Type Criterion for Radial Functions of Several Variables
• Scattering matrices and Weyl functions
• Self-adjoint extensions of restrictions
• On positive definiteness of some functions

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