On Hankel determinants of functions given by their expansions in $P$-fractions

  • V. I. Buslaev Мат. ин-т РАН, Москва, Россия

Abstract

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.
Published
25.03.2010
How to Cite
Buslaev, V. I. “On Hankel Determinants of Functions Given by Their Expansions in $P$-Fractions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 3, Mar. 2010, pp. 315–326, https://umj.imath.kiev.ua/index.php/umj/article/view/2870.
Section
Research articles