On meromorphic approximation

Let G be a bounded N-connected domain, the boundary Gamma of which consists of closed analytic Jordan curves. We assume that 0 is an element of G. For any nonnegative integers n and m, denote by M-n,M-m the class of all meromorphic functions on G that can be represented in the form h = p/qz(m), where p belongs to the Smirnov class E-infinity(G), q is a polynomial of degree at most n, q not equivalent to 0. Theorems giving necessary and sufficient conditions for a function belonging to the class M-n,M-m to be an element of best approximation to a continuous function f on Gamma in the space L-infinity(Gamma) by functions in the class M-n,M-m are proved. Some questions concerning orthogonal polynomials and the theory of Hankel operators are also considered.