Direct and inverse spectral theory of singular left-definite Sturm-Liouville operators

DOI10.1016/j.jde.2012.04.006zbMath1250.34021arXiv1110.5195OpenAlexW2025528368MaRDI QIDQ432446

Jonathan Eckhardt

Publication date: 4 July 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5195

zbMATH Keywords

spectral theorySturm-Liouville theoryleft-definite problems

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Weyl theory and its generalizations for ordinary differential equations (34B20) General spectral theory of ordinary differential operators (34L05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Inverse problems involving ordinary differential equations (34A55) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items (13)

The inverse spectral problem for indefinite strings ⋮ Spectral properties of singular Sturm-Liouville operators via boundary triples and perturbation theory ⋮ Inverse uniqueness results for Schrödinger operators using de Branges theory ⋮ Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators ⋮ Scattering and inverse scattering for a left-definite Sturm-Liouville problem ⋮ A class of \({n}\)-entire Schrödinger operators ⋮ The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data ⋮ Unique solvability of a coupling problem for entire functions ⋮ Mixed data in inverse spectral problems for the Schrödinger operators ⋮ On the absolutely continuous spectrum of generalized indefinite strings ⋮ On spectral deformations and singular Weyl functions for one-dimensional Dirac operators ⋮ On the absolutely continuous spectrum of generalized indefinite strings. II ⋮ Quadratic operator pencils associated with the conservative Camassa-Holm flow

Cites Work

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• Sturm-Liouville operators with measure-valued coefficients
• Operational calculus of linear relations
• A general approach to approximation problems of the Bernstein type
• Global conservative solutions of the Camassa-Holm equation
• Self-adjoint extensions of symmetric subspaces
• Weighted \(L^p\) closure theorems for spaces of entire functions
• A remark to the ordering theorem of L. de Branges
• Global weak solutions for a shallow water equation
• Multipeakons and the classical moment problem
• A limit point criterion with applications to nonselfadjoint equations
• On the substitution rule for Lebesgue-Stieltjes integrals
• On the isospectral problem of the dispersionless Camassa-Holm equation
• The functional calculus for sectorial operators
• On the scattering problem for the Camassa-Holm equation
• Inverse Spectral and Scattering Theory for the Half-Line Left-Definite Sturm–Liouville Problem
• Stability of peakons
• On the Spectral Problem Associated with the Camassa-Holm Equation
• Spectral Asymptotics for Sturm-Liouville Equations
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• On spectral theory for Schrödinger operators with strongly singular potentials

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