Приближение интегралов типа Коши в жордановых областях

Abstract

The notion of a generalized y-derivative of a function of complex variable is introduced and applied to classifying the functions analytic in Jordan domains. The approximations of functions from thus introduced classes are studied by using algebraic polynomials constructed on the basis of Faber polynomials by the summation of Faber scries. In the periodic case, the analogues of author's results are obtained for the classes Lψβℜ.