On the reconstruction of a convolution perturbation of the Sturm-Liouville operator from the spectrum

DOI10.1134/S0012266110010167zbMath1197.34017MaRDI QIDQ981749

Sergey Buterin

Publication date: 2 July 2010

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

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse problems involving ordinary differential equations (34A55)

Related Items (28)

Inverse spectral problems for first order integro-differential operators ⋮ Reconstruction of the Volterra-type integro-differential operator from nodal points ⋮ On uniqueness of recovering the convolution integro-differential operator from the spectrum of its non-smooth one-dimensional perturbation ⋮ Inverse problems of recovering first-order integro-differential operators from spectra ⋮ On an inverse spectral problem for one integro-differential operator of fractional order ⋮ Inverse spectral problem for integro-differential Sturm-Liouville operators with discontinuity conditions ⋮ Uniform full stability of recovering convolutional perturbation of the Sturm-Liouville operator from the spectrum ⋮ Uniform stability of the inverse spectral problem for a convolution integro-differential operator ⋮ On recovering the Dirac operator with an integral delay from the spectrum ⋮ Inverse problems for second order integro-differential operators ⋮ An inverse spectral problem for Sturm-Liouville operators with frozen argument ⋮ An inverse problem for the integro-differential Dirac system with partial information given on the convolution kernel ⋮ On an inverse spectral problem for first-order integro-differential operators with discontinuities ⋮ Numerical solution and stability of the inverse spectral problem for a convolution integro-differential operator ⋮ On Recovering Integro-Differential Operators from the Weyl Function ⋮ On a Transformation Operator Approach in the Inverse Spectral Theory of Integral and Integro-Differential Operators ⋮ On the half inverse spectral problem for an integro-differential operator ⋮ On inverse problem for a convolution integro-differential operator with Robin boundary conditions ⋮ On global solvability and uniform stability of one nonlinear integral equation ⋮ Inverse problems for first-order integro-differential operators ⋮ A trace formula for integro-differential operators on the finite interval ⋮ An inverse spectral problem for Sturm-Liouville operators with a large constant delay ⋮ Inverse problems for second order integral and integro-differential operators ⋮ On solvability of one nonlinear integral equation in the class of analytic functions ⋮ Inverse problems for arbitrary order integral and integro-differential operators ⋮ On Borg's method for non-selfadjoint Sturm-Liouville operators ⋮ An inverse spectral problem for integro-differential Dirac operators with general convolution kernels ⋮ Unnamed Item

Cites Work

• Method of spectral mappings in the inverse problem theory
• Inverse spectral reconstruction problem for the convolution operator perturbed by a one-dimensional operator
• The inverse spectral problem for integro-differential operators
• On an inverse spectral problem for a convolution integro-differential operator
• Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
• The inverse problem of recovering the Volterra convolution operator from the incomplete spectrum of its rank-one perturbation
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