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

Autor:	Derkach, V., Kovalyov, I.
Rok vydání:	2020
Předmět:	Mathematics - Spectral Theory Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.07456 Zobrazit plný text záznamu View this record from Arxiv