Inverse eigenvalue problems for a damped Stieltjes string with mixed data - Yang, Lu; Guo, Yongxia; Wei, Guangsheng (Linear algebra and its applications, 2020)
In this paper, we consider the inverse eigenvalue problem for a Stieltjes string subject to the Robin condition at the left end and a damping condition at the right end with mixed data, which consists of the values of a part of masses and lengths and a subset of its spectrum. We use Krein-Nudelman's interpolation formula for a rational S-function to deal with our problem. We present a decomposition of the S0-function associated with the Stieltjes string, which makes it possible to use Krein-Nudelman's interpolation formula. Necessary and sufficient conditions are given for existence and uniqueness of solution to the inverse problem such that a finite number of simple not purely imaginary complex numbers lying in the open upper half-plane are a subset of the spectrum of a damped Stieltjes string.