Geodesic
On the Van Vleck theorem for regular $C$-fractions with limit-periodic coefficients
Izvestiya. Mathematics , Tome 65 (2001) no. 4, pp. 673-686

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In this paper we investigate the convergence set of a regular $C$-fraction with limit-periodic coefficients. This investigation is based on a general assertion concerning the convergence of composites of linear-fractional transformations whose coefficients are limit-periodic functions depending holomorphically on a parameter. We show that the singularity set of such a $C$-fraction possesses an extremal property stated in terms of the transfinite diameter (capacity) of sets. 
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     author = {V. I. Buslaev},
     title = {On the {Van} {Vleck} theorem for regular $C$-fractions with limit-periodic coefficients},
     journal = {Izvestiya. Mathematics },
     pages = {673--686},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_4_a2/}
}
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V. I. Buslaev. On the Van Vleck theorem for regular $C$-fractions with limit-periodic coefficients. Izvestiya. Mathematics , Tome 65 (2001) no. 4, pp. 673-686. http://geodesic.mathdoc.fr/item/IM2_2001_65_4_a2/