1-D Schrödinger operators with local point interactions on a discrete set
Aleksey Kostenko,Mark Malamud +1 more
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In this article, the authors considered the case d ∗ = 0 and obtained necessary and sufficient conditions for the operators H X, α to be self-adjoint, lower semibounded, and discrete.About:
This article is published in Journal of Differential Equations.The article was published on 2010-07-15 and is currently open access. It has received 128 citations till now.read more
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Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
TL;DR: In this paper, the authors systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals (a, b) associated with rather general differential expressions of the type \[ ======\tau f = \frac{1}{r} (- \big(p[f' + s f]\big)' + s p[f+s f] + qf),] where the coefficients $p, $q, $r, $s$ are real-valued and Lebesgue measurable on $(a,b)$, with $
Journal ArticleDOI
Spectral theory of semibounded Sturm–Liouville operators with local interactions on a discrete set
TL;DR: In this article, Kostenko et al. showed that the Hamiltonians HX,α,q with δ-type point interactions at the centers xk on the positive half line in terms of energy forms are self-adjoint if they are lower semibounded.
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Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples
Jussi Behrndt,Matthias Langer +1 more
TL;DR: In this paper, the notion of quasi boundary triples and their Weyl functions is reviewed and applied to self-adjointness and spectral problems for a class of elliptic, formally symmetric, second order partial differential expressions with variable coefficients on bounded domains.
Journal ArticleDOI
Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials
TL;DR: In this paper, the authors systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals and derive the corresponding spectral transformation, including a characterization of spectral multiplicities and minimal supports of standard subsets of the spectrum.
Journal ArticleDOI
Schrödinger operators with δ- and δ′-interactions on Lipschitz surfaces and chromatic numbers of associated partitions
TL;DR: In this paper, the authors investigated Schrodinger operators with δ- and δ′-interactions supported on hypersurfaces, which separate the Euclidean space into finitely many bounded and unbounded Lipschitz domains.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
Theory of linear operators in Hilbert space
N. I. Akhiezer,I. M. Glazman +1 more
TL;DR: In this article, the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators in hilbert spaces are discussed, as well as the stability of self-jointness under small perturbations.
Book
Solvable Models in Quantum Mechanics
TL;DR: The one-center point interaction as discussed by the authors is a special case of the Coulomb point interaction, where Coulomb plus one center point interaction in three dimensions plus Coulomb and one center interaction in two dimensions.