Abstract:
In 1918, I.Schur described an algorithm that allows one to represent a Schur function (i.e. a function that is holomorphic in the circle $|z|<1$ and takes values in the closure of this circle) as a Schur continued fraction. The multipoint Schur algorithm, unlike the classical one, in which all interpolation points are concentrated at zero, represents the Schur function as a multipoint Schur continued fraction, in which the interpolation points are a predetermined sequence of points on the circle $|z|<1$. The report will show that the well-known results of I. Schur and J. L. Geronimus on the convergence of classical Schur continued fractions with certain conditions on their coefficients also hold in the case of multipoint Schur continued fractions.
