Direct and Inverse Spectral Assignment for the Operator Sturm-Liuoville type with Linear Delay

Abstract

In this paper, we constructed the solution of the spectral boundary problem on [0, π] with zero initial function and separated boundary conditions. In this work, characteristic function is constructed and asymptotics of its large zeroes and eigenvalues asymptotics of the operator are found. In the second part of this paper, it is assumed that two sets of eigenvalues are given when h = 0. Under certain conditions of the linear delay, the parameters of operators are found. It means that we solved the inverse spectral problem using a Fouriers series method.