TY - JOUR
AU - V. I. Buslaev
PY - 2010/03/25
Y2 - 2024/10/08
TI - On Hankel determinants of functions given by their expansions in $P$-fractions
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 62
IS - 3
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2870
AB - We obtain explicit formulas that express the Hankel determinants of functions given by their expansions in continued $P$-fractions in terms of the parameters of the fraction. As a corollary, we obtain a lower bound for the capacity of the set of singular points of these functions, an analog of the van Vleck theorem for $P$-fractions with limit-periodic coefficients, another proof of the Gonchar theorem on the Leighton conjecture, and an upper bound for the radius of the disk of meromorphy of a function given by a $С$-fraction.
ER -