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Full indefinite Stieltjes moment problem and Padé approximants


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


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Article Information

TitleFull indefinite Stieltjes moment problem and Padé approximants
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 1, 1-26
MilestonesReceived 15/10/2019; Revised 18/02/2020
CopyrightThe 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


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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},
       URL = {http://mfat.imath.kiev.ua/article/?id=1285},
}


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