On the representation of algebraic functions by continued $J$-fractions

The problem of representation of analytic functions by continued $J$-fractions is the classical problem analysis. On the talk this problem will be discussed from the contemporary point of view, when $n$-th convergent to a continued fraction considered as $n$-th diagonal Pade approximation. We shall discuss the most prominent result in that direction: Stahl's Theorem on the representation of an arbitrary algebraic function via continued fraction.