English

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.

Keywords

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

R2 v1 2026-06-23T13:45:03.950Z