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.
Key words: Indefinite Stieltjes moment problem, generalized Stieltjes function,
gene\-ralized Stieltjes polynomials, Schur algorithm,
resolvent matrix
Full Text
Article Information
| Title | Full indefinite Stieltjes moment problem and Padé approximants |
| Source | Methods Funct. Anal. Topology, Vol. 26 (2020), no. 1, 1-26 |
| DOI | 10.31392/MFAT-npu26_1.2020.01 |
| MathSciNet |
MR4113578 |
| Milestones | Received 15/10/2019; Revised 18/02/2020 |
| Copyright | The Author(s) 2020 (CC BY-SA) |
Authors Information
Volodymyr Derkach
Vasyl′ Stus Donetsk National University, 21, 600-richchia str., Vinnytsia, 21021, Ukraine
Ivan Kovalyov
Dragomanov National Pedagogical University, 9, Pyrogova str., Kyiv, 01601, Ukraine
Citation Example
Volodymyr Derkach and Ivan Kovalyov, Full indefinite Stieltjes moment problem and Padé approximants, Methods Funct. Anal. Topology 26
(2020), no. 1, 1-26.
BibTex
@article {MFAT1285,
AUTHOR = {Volodymyr Derkach and Ivan Kovalyov},
TITLE = {Full indefinite Stieltjes moment problem and Padé approximants},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {26},
YEAR = {2020},
NUMBER = {1},
PAGES = {1-26},
ISSN = {1029-3531},
MRNUMBER = {MR4113578},
DOI = {10.31392/MFAT-npu26_1.2020.01},
URL = {http://mfat.imath.kiev.ua/article/?id=1285},
}
