Abstract
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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