On a class of generalized Stieltjes continued fractions

Abstract

With each sequence of real numbers ${\mathbf s}=\{s_j\}_{j=0}^\infty$ two kinds of continued fractions are associated, - the so-called $P-$fraction and a generalized Stieltjes fraction that, in the case when ${\mathbf s}=\{s_j\}_{j=0}^\infty$ is a sequence of moments of a probability measure on $\mathbb R_+$, coincide with the $J-$fraction and the Stieltjes fraction, respectively. A subclass $\mathcal H^{reg}$ of regular sequences is specified for which explicit formulas connecting these two continued fractions are found. For ${\mathbf s}\in\mathcal H^{reg}$ the Darboux transformation of the corresponding generalized Jacobi matrix is calculated in terms of the generalized Stieltjes fraction.

Key words: Moment problem, continued fraction, generalized Stieltjes fraction, Darboux transformation, generalized Jacobi matrix, triangular factorization, unwrapping transformation.

Full Text

Article Information

Title	On a class of generalized Stieltjes continued fractions
Source	Methods Funct. Anal. Topology, Vol. 21 (2015), no. 4, 315-335
MathSciNet	MR3469531
zbMATH	06630277
Milestones	Received 02/02/2015; Revised 05/03/2015
Copyright	The Author(s) 2015 (CC BY-SA)

Authors Information

Vladimir Derkach
Department of Mathematics, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka,Ivano-Frankivsk, 76018, Ukraine

Ivan Kovalyov
Department of Mathematics, Dragomanov National Pedagogical University, 9 Pirogova, Kyiv, 01601, Ukraine

Citation Example

Vladimir Derkach and Ivan Kovalyov, On a class of generalized Stieltjes continued fractions, Methods Funct. Anal. Topology 21 (2015), no. 4, 315-335.

BibTex

@article {MFAT781,
    AUTHOR = {Derkach, Vladimir and Kovalyov, Ivan},
     TITLE = {On a class of generalized Stieltjes continued fractions},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {21},
      YEAR = {2015},
    NUMBER = {4},
     PAGES = {315-335},
      ISSN = {1029-3531},
  MRNUMBER = {MR3469531},
 ZBLNUMBER = {06630277},
       URL = {http://mfat.imath.kiev.ua/article/?id=781},
}

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