ON FUNCTIONS WITH SIMILAR VALUES FOR MINIMAL DEVIATIONS FROM POLYNOMIALS AND RATIONAL FUNCTIONS

Abstract

The author establishes that, for every function that is analytic inside the unit disk and belongs to the space with 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>, the equation is satisfied, where and are the minimal deviations of from polynomials of degree at most and from rational functions of order at most . In particular, if and only if can be continued analytically over the disk .There is also a similar proposition for the approximation of functions in the spaces , 1$ SRC=http://ej.iop.org/images/0025-5734/74/2/A07/tex_sm_3353_img4.gif/>.