Geodesic
Convergence of a Limit Periodic Schur Continued Fraction
Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 643-656

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In this paper, we show that if the parameters of a Schur continued fraction tend to zero, then the functions to which the even convergents converge inside the unit disk and the functions to which the odd convergents converge outside the unit disk cannot have a meromorphic continuation to each other through any arc of the unit circle. This result is obtained as a consequence of the convergence theorem for limit periodic Schur continued fractions.
Keywords: continued fractions, Hankel determinants, transfinite diameter, meromorphic continuation. 
@article{MZM_2020_107_5_a0,
     author = {V. I. Buslaev},
     title = {Convergence of a {Limit} {Periodic} {Schur} {Continued} {Fraction}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--656},
     publisher = {mathdoc},
     volume = {107},
     number = {5},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a0/}
}
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V. I. Buslaev. Convergence of a Limit Periodic Schur Continued Fraction. Matematičeskie zametki, Tome 107 (2020) no. 5, pp. 643-656. http://geodesic.mathdoc.fr/item/MZM_2020_107_5_a0/