Some examples in approximation on the unit disk by reciprocals of polynomials
This paper is a continuation of the authors’ study of approximation by reciprocals of polynomials. A Jackson-type theorem for such approximants is established for a certain class of functions f analytic and nonzero in the disk |z|<1 and continuous on |z|≤1. Furthermore, we obtain the sharp degree of convergence for reciprocal polynomial approximation on |z|≤1 to functions f that are analytic on |z|≤1, nonzero in |z|<1, and vanish somewhere on |z|=1.
AMS subject classification 41A2041A17
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