Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definite functions

DOI10.1016/J.JFA.2012.07.019zbMath1256.35030arXiv1208.1203OpenAlexW2963349231MaRDI QIDQ1762337

Konrad Schmüdgen, Mark M. Malamud

Publication date: 23 November 2012

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.1203

zbMATH Keywords

Schrödinger operatorspectrumpositive definite functionpoint interactionsself-adjoint extension

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Positive definite functions on groups, semigroups, etc. (43A35)

Related Items (16)

Schrödinger operators with δ- and δ′-interactions on Lipschitz surfaces and chromatic numbers of associated partitions ⋮ Invariant Schrödinger operators with point interactions at the vertices of a regular polyhedron ⋮ To the theory of nonnegative point Hamiltonians on a plane and in the space ⋮ On the Birman problem in the theory of nonnegative symmetric operators with compact inverse ⋮ Bound states of the spin-orbit coupled ultracold atom in a one-dimensional short-range potential ⋮ Boundary pairs associated with quadratic forms ⋮ On the criteria of transversality and disjointness of nonnegative self-adjoint extensions of nonnegative symmetric operators ⋮ Boundary triplets, tensor products and point contacts to reservoirs ⋮ A self-adjointness criterion for the Schrödinger operator with infinitely many point interactions and its application to random operators ⋮ Infinitely many singular interactions on noncompact manifolds ⋮ Strictly and strongly positive definite functions on locally compact hypergroups ⋮ Schoenberg matrices of radial positive definite functions and Riesz sequences of translates in \(L^2(\mathbb R^n)\) ⋮ Unnamed Item ⋮ Point interactions in a line and the Riesz bases of \(\delta\)-functions ⋮ Asymptotics of Random Resonances Generated by a Point Process of Delta-Interactions ⋮ Series expansion for the Fourier transform of a rational function in three dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sturm-Liouville boundary value problems with operator potentials and unitary equivalence
• On the unitary equivalence of absolutely continuous parts of self-adjoint extensions
• Kreĭn-like extensions and the lower boundedness problem for elliptic operators
• Weyl function and spectral properties of self-adjoint extensions
• The spectrum of defect periodic point interactions
• Spectral theory for perturbed Krein Laplacians in nonsmooth domains
• Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrödinger operators revisited
• Spectral theory of elliptic operators in exterior domains
• 1-D Schrödinger operators with local point interactions on a discrete set
• On symmetries in the theory of finite rank singular perturbations
• Generalized resolvents and the boundary value problems for Hermitian operators with gaps
• Certain classes of extensions of a lacunary Hermitian operator
• The von Neumann problem for nonnegative symmetric operators
• Elliptic operators with boundary conditions on a subset of measure zero
• On the connection between exponential bases and certain related sequences in \(L^ 2 (-\pi, \pi)\)
• The band structure of the general periodic Schrödinger operator with point interactions
• Necessary density conditions for sampling an interpolation of certain entire functions
• Spherical distributions: Schoenberg (1938) revisited
• Metric spaces and completely monontone functions
• A Criterion for a Characteristic Function and a Polyá-Type Criterion for Radial Functions of Several Variables
• SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
• Scattering matrices and Weyl functions
• Distributions and Operators
• Self-adjoint extensions of restrictions
• On the Schrödinger operator with periodic point interactions in the three-dimensional case
• On a class of Riesz-Fischer sequences
• Radial positive definite functions and spectral theory of the Schrödinger operators with point interactions
• Spectral theory of semibounded Sturm–Liouville operators with local interactions on a discrete set
• On general boundary problems for elliptic differential equations
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Metric Spaces and Positive Definite Functions
• On positive definiteness of some functions
• A Krein-like formula for singular perturbations of self-adjoint operators and applications

This page was built for publication: Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definite functions