Full indefinite Stieltjes moment problem and Padé approximants

Authors

  • V. A. Derkach Vasyl′ Stus Donetsk National University, 21, 600-richchia str., Vinnytsia, 21021, Ukraine
  • I. Kovalyov Dragomanov National Pedagogical University, 9, Pyrogova str., Kyiv, 01601, Ukraine

DOI:

https://doi.org/https://doi.org/10.31392/MFAT-npu26_1.2020.01

Keywords:

Indefinite Stieltjes moment problem, generalized Stieltjes function, gene\-ralized Stieltjes polynomials, Schur algorithm, resolvent matrix

Abstract

Full indefinite Stieltjes moment problem is studied via the step-by-step Schur algorithm. Naturally associated with indefinite Stieltjes moment problem are generalized Stieltjes continued fraction and a system of difference equations, which, in turn, lead to factorization of resolvent matrices of indefinite Stieltjes moment problem. A criterion for such a problem to be indeterminate in terms of continued fraction is found and a complete description of its solutions is given in the indeterminate case. Explicit formulas for diagonal and sub-diagonal Padé approximants for formal power series corresponding to indefinite Stieltjes moment problem and convergence results for Padé approximants are presented.

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Published

2020-03-25

Issue

Vol. 26 No. 1 (2020)

Section

Articles

How to Cite

Derkach, V. A., and I. Kovalyov. “Full Indefinite Stieltjes Moment Problem and Padé Approximants”. Methods of Functional Analysis and Topology, vol. 26, no. 1, Mar. 2020, pp. 1-26, https://doi.org/https://doi.org/10.31392/MFAT-npu26_1.2020.01.