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arXiv · 2002.07456

Full indefinite Stieltjes moment problem and Pad\'{e} approximants

V. Derkach·I. Kovalyov
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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.

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V. Derkach, I. Kovalyov. 2020-02-18. Full indefinite Stieltjes moment problem and Pad\'{e} approximants. https://arxiv.org/abs/2002.07456

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