Solution of the inverse spectral problem for a convolution integro-differential operator with Robin boundary conditions

Abstract

The operator of double differentiation on a finite interval with Robin boundary conditions perturbed by the composition of a Volterra convolution operator and the differentiation one is considered. We study the inverse problem of recovering the convolution kernel along with a coefficient of the boundary conditions from the spectrum. We prove the uniqueness theorem and that the standard asymptotics is a necessary and sufficient condition for an arbitrary sequence of complex numbers to be the spectrum of such an operator. A constructive procedure for solving the inverse problem is given.

10 pages

References in corpus (3)

• Solution of the inverse spectral problem for a convolution integro-differential operator with Robin boundary conditions
• Recovering Differential Operators with Nonseparated Boundary Conditions in the Central Symmetric Case
• Recovering Differential Operators with Nonlocal Boundary Conditions

Cited by in corpus (3)

• On recovering Sturm-Liouville operators with frozen argument from the spectrum
• Solution of the inverse spectral problem for a convolution integro-differential operator with Robin boundary conditions
• Uniform stability of the inverse spectral problem for a convolution integro-differential operator