APPROXIMATION BY A POLYNOMIAL AND ITS DERIVATIVES ON CERTAIN CLOSED SETS

The work on the theory of approximations initiated by Weierstrass and continued by Walsh, Keldysh, and Lavrentiev, among others, has culminated in the following theorem of Mergelyan (See Mergelyan [3]): Given any compact subset C of the complex plane, which does not separate the plane, and given any continuous function f on C which is analytic interior to C, then f can be approximated uniformly on C by polynomials…