A practical method for recovering Sturm–Liouville problems from the Weyl function

DOI10.1088/1361-6420/abff06OpenAlexW3163658416MaRDI QIDQ4993903

Sergii M. Torba, Vladislav V. Kravchenko

Publication date: 11 June 2021

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.08930

zbMATH Keywords

inverse spectral problemGelfand-Levitan equationWeyl-Titchmarsh theoryNeumann series of Bessel functionstransmutation operatorSturm-Liouville spectral problem

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Weyl theory and its generalizations for ordinary differential equations (34B20) Inverse problems involving ordinary differential equations (34A55)

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Local solvability and stability of the generalized inverse Robin-Regge problem with complex coefficients, Recovery of a potential on a quantum star graph from Weyl's matrix, Spectrum completion and inverse Sturm–Liouville problems, Professor Vladislav V. Kravchenko: a mathematician and a friend, Reconstruction techniques for complex potentials

Cites Work

• Reconstruction of the potential of the Sturm-Liouville operator from a finite set of eigenvalues and normalizing constants
• An inverse problem by eigenvalues of four spectra
• Transmutations, \(L\)-bases and complete families of solutions of the stationary Schrödinger equation in the plane
• Boundary problems for ordinary differential equations with parameter in the boundary conditions
• Enclosing solutions of an inverse Sturm-Liouville problem with finite data
• Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions
• A Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations
• A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure
• A new approach to inverse spectral theory. I: Fundamental formalism
• A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications
• Inverse Sturm-Liouville problem with analytical functions in the boundary condition
• Transmutations, singular and fractional differential equations with applications to mathematical physics
• An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition
• On a method for solving the inverse Sturm-Liouville problem
• Inverse spectral problems and closed exponential systems
• Determination of partially known Sturm-Liouville potentials
• Discrete and continuous boundary problems
• On the inverse spectral theory of Schrödinger and Dirac operators
• An Inverse Sturm–Liouville Problem with Mixed Given Data
• Reconstruction Techniques for Classical Inverse Sturm-Liouville Problems
• An Introduction to Inverse Scattering and Inverse Spectral Problems
• The inverse sturm‐liouville problem
• Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum
• Operator Theory and Harmonic Analysis
• Direct and Inverse Sturm-Liouville Problems
• Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition
• A direct method for solving inverse Sturm–Liouville problems*
• On the solution of the static Maxwell system in axially symmetric inhomogeneous media
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