Abstract
Letf(z) be analytic in the interior of a rectifiable Jordan curve C and continuous in the corresponding closed region C. The relation between continuity properties of f(z) on C and degree of approximarion to f(z) by polynomials -rT(z) in z of respective degrees n, n = 1, 2, * * *, has been extensively studied. In the present paper we study the relation between continuity properties of f(z) on C and degree of approximation to f(z) on C by rational functions r (z) in z of respective degrees n whose poles lie exterior to C. We thus deal with what is frequently referred to in the theory as Problem oz.
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