Inverse spectral problem for differential pencils with a frozen argument
Abstract
This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the boundary conditions and the position of argument, we describe two cases: degenerate and non-degenerate. For these two cases, the uniqueness of inverse spectral problem are studied and a constructive procedure for reconstructing the potentials along with necessary and sufficient conditions of its solvability are obtained.
Keywords
Cite
@article{arxiv.2305.02529,
title = {Inverse spectral problem for differential pencils with a frozen argument},
author = {Yi-teng Hu and Murat Sat},
journal= {arXiv preprint arXiv:2305.02529},
year = {2024}
}
Comments
In the arxiv version of this manuscript, the Lemma 3.4 is not correct, which should be proved. Since the Hadamard's factorization is important for the reconstrucion of potentials, while for the first formulae, we should prove it again