Editorial Introduction

Abstract

In 1917/1918 Issai Schur published two papers “On the power series which are bounded in the interior of the unit circle, I and II” in the “Journal fuer Reine und Angewandte Mathematik.” In these two papers the author solved a number of important interpolation problems for classes of analytic functions in the disc. One of them in the famous Schur problem: given complex numbers c₀, c₁, ... c_n find a function

$$ f\left( x \right) = \sum\limits_{j = 0}^n {{c_j}{x^j} + \sum\limits_{j = n + 1}^\infty {{f_j}{x^j}} } $$

which is both analytic and bounded by one: |f(x)| ≤ 1, in the disc |x| < 1.