Regularization of the indefinite Stieltjes moment problem

α − regular indefinite Stieltjes moment problem and Darboux transformation

“…Definition 2.1. ( [16]) We say that a sequence \bfs = \{ s i \} \ell i=0 belongs to the \alpha - regular class \scrH k,\alpha - reg \kappa ,\ell , if \bfs \in \scrH k \kappa ,\ell and all polynomials of the first kind P nj associated with the sequence \bfs satisfy the following condition: P nj (\alpha ) \not = 0 for all n j \in \scrN (\bfs ).…”

“…As was shown in [16,Lemma 5.4], the Stieltjes polynomials are solutions of the following system, and S - fraction (2.25) is also associated with the following system of difference equations:…”

“…Indefinite moment problems in the classes \bfN \kappa were studied in [3,20]. Indefinite moment problems in the classes \bfN + \kappa and \bfN k \kappa were studied in [20,21] and [5,6,7,8,9,14,16], respectively.…”

“…In this paper, we study the \alpha - regular indefinite moment problem in the generalized Stieltjes class and its connection with the Darboux transformation. It is based on the results of [15,16]. New formulas for the Stieltjes polynomials are found in the Section 3, and then we obtain a description of a solution of the \alpha - regular indefinite moment problem MP k \kappa (s, \ell ).…”

Rational generalized Stieltjes functions

“…The indefinite Hamburger moment in the generalized Nevanlinna class N κ was studied in [10]. The indefinite Stieltjes moment problem in the generalized Stieltjes class N k κ was studied in [11], [1], [2], [6] and [7]. One is based on the Schur algorithm, i.e.…”