Solution of the inverse spectral problem for a convolution integro-differential operator with Robin boundary conditions
Spectral Theory
2020-01-28 v1
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.
Cite
@article{arxiv.1504.06052,
title = {Solution of the inverse spectral problem for a convolution integro-differential operator with Robin boundary conditions},
author = {S. A. Buterin and A. E. Choque Rivero},
journal= {arXiv preprint arXiv:1504.06052},
year = {2020}
}
Comments
10 pages