Full indefinite Stieltjes moment problem and Pad\'{e} approximants
Spectral Theory
2020-02-19 v1 Classical Analysis and ODEs
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 formulae for diagonal and sub-diagonal Pad\'{e} approximants for formal power series corresponding to indefinite Stieltjes moment problem and convergence results for Pad\'{e} approximants are presented.
Cite
@article{arxiv.2002.07456,
title = {Full indefinite Stieltjes moment problem and Pad\'{e} approximants},
author = {V. Derkach and I. Kovalyov},
journal= {arXiv preprint arXiv:2002.07456},
year = {2020}
}
Comments
29 pages