Geodesic
Schur's criterion for formal power series
Sbornik. Mathematics, Tome 210 (2019) no. 11, pp. 1563-1580 Cet article a éte moissonné depuis la source Math-Net.Ru

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A criterion for when a formal power series can be represented by a formal Schur continued fraction is stated. The proof proposed is based on a relationship, revealed here, between Hankel two-point determinants of a series and its Schur determinants. Bibliography: 10 titles.
Keywords: continued fractions, Schur functions, Hankel determinants. 
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V. I. Buslaev. Schur's criterion for formal power series. Sbornik. Mathematics, Tome 210 (2019) no. 11, pp. 1563-1580. http://geodesic.mathdoc.fr/item/SM_2019_210_11_a2/

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[2] J. Schur, “Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind”, J. Reine Angew. Math., 1917:147 (1917), 205–232 ; 1918:148 (1918), 122–145 | DOI | MR | Zbl | DOI | MR

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[4] V. I. Buslaev, “On the convergence of continued T-fractions”, Proc. Steklov Inst. Math., 235 (2001), 29–43 | MR | Zbl

[5] V. I. Buslaev, “On Hankel determinants of functions given by their expansions in $P$-fractions”, Ukrainian Math. J., 62:3 (2010), 358–372 | DOI | MR | Zbl

[6] V. I. Buslaev, “Otsenka emkosti mnozhestva osobennostei funktsii, zadannykh svoim razlozheniem v nepreryvnuyu drob”, Anal. Math., 39:1 (2013), 1–27 | DOI | MR | Zbl

[7] V. I. Buslaev, “An analog of Gonchar's theorem for the $m$-point version of Leighton's conjecture”, Proc. Steklov Inst. Math., 293 (2016), 127–139 | DOI | DOI | MR | Zbl

[8] V. I. Buslaev, “On the Van Vleck theorem for limit-periodic continued fractions of general form”, Proc. Steklov Inst. Math., 298 (2017), 68–93 | DOI | DOI | MR | Zbl

[9] V. I. Buslaev, “On singular points of meromorphic functions determined by continued fractions”, Math. Notes, 103:4 (2018), 527–536 | DOI | DOI | MR | Zbl

[10] V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205 | DOI | DOI | MR | Zbl