Weyl-Titchmarsh Theory for Schrodinger Operators with Strongly Singular Potentials

From MaRDI portal
Publication:2883871

DOI10.1093/imrn/rnr065zbMath1248.34027arXiv1007.0136OpenAlexW3099270621WikidataQ57343663 ScholiaQ57343663MaRDI QIDQ2883871

Gerald Teschl, Alexander L. Sakhnovich, Aleksey S. Kostenko

Publication date: 14 May 2012

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0136




Related Items (41)

Explicit solutions of matrix and dynamical Schrödinger equations and of KdV equation in terms of square roots of the generalised matrix eigenvaluesOn the Weyl solution of the 1-dim Schrödinger operator with inverse fourth power potentialTitchmarsh-Weyl theory for Schrödinger operators on unbounded domainsOn the asymptotics of the spectral density of radial Dirac operators with divergent potentialEigenfunction expansions for the Schrödinger equation with an inverse-square potentialInverse scattering at fixed energy on asymptotically hyperbolic Liouville surfacesReduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm modelSpectral asymptotics for perturbed spherical Schrödinger operators and applications to quantum scatteringDispersion estimates for spherical Schrödinger equationsWeyl functions of generalized Dirac systems: integral representation, the inverse problem and discrete interpolationCoupling constant dependence for the Schrödinger equation with an inverse-square potentialStability in the inverse Steklov problem on warped product Riemannian manifoldsA Gronwall-type Trigonometric InequalityStationary and dynamical scattering problems and ergodic-type theoremsSpectral analysis of selfadjoint elliptic differential operators, Dirichlet-to-Neumann maps, and abstract Weyl functionsSturm-Liouville operators with measure-valued coefficientsOn the substitution rule for Lebesgue-Stieltjes integralsInverse uniqueness results for Schrödinger operators using de Branges theorySingular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operatorsCorrigendum to ``Inverse spectral theory for a singular Sturm-Liouville operator on \([0,1\) [J. Differential Equations 76 (2) (1988) 353-373]] ⋮ On self-adjoint boundary conditions for singular Sturm-Liouville operators bounded from belowNon-uniqueness results for the anisotropic Calderón problem with data measured on disjoint setsUniqueness from discrete data in an inverse spectral problem for a pencil of ordinary differential operatorsInitial value problems for integrable systems on a semi-stripDirect and inverse spectral theorems for a class of canonical systems with two singular endpointsOn the singular Weyl-Titchmarsh function of perturbed spherical Schrödinger operatorsSpectral asymptotics for canonical systemsRegular singular Sturm-Liouville operators and their zeta-determinantsNonlinear Schrödinger equation in a semi-strip: evolution of the Weyl-Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditionsOn the hidden mechanism behind non-uniqueness for the anisotropic Calderón problem with data on disjoint setsA class of \({n}\)-entire Schrödinger operatorsOn Fourier transforms of radial functions and distributionsOn the spectral theory of the Bessel operator on a finite interval and the half-lineAn operator theoretic interpretation of the generalized Titchmarsh-Weyl function for perturbed spherical Schrödinger operatorsMark Krein's method of directing functionals and singular potentialsSingular Schrödinger operators as self-adjoint extensions of 𝑁-entire operatorsMixed data in inverse spectral problems for the Schrödinger operatorsTransformation operators for spherical Schrödinger operatorsOn spectral deformations and singular Weyl functions for one-dimensional Dirac operatorsUniqueness results for one-dimensional Schrödinger operators with purely discrete spectraQuadratic operator pencils associated with the conservative Camassa-Holm flow




This page was built for publication: Weyl-Titchmarsh Theory for Schrodinger Operators with Strongly Singular Potentials