Approximation by simple partial fractions in unbounded domains

For unbounded simply connected domains $D$ in the complex plane, bounded by several simple curves with regular asymptotic behaviour at infinity, we obtain necessary conditions and sufficient conditions for simple partial fractions (logarithmic derivatives of polynomials) with poles on the boundary of $D$ to be dense in the space of holomorphic functions in $D$ (with the topology of uniform convergence on compact subsets of $D$). In the case of a strip $\Pi$ bounded by two parallel lines, we give estimates for the convergence rate to zero in the interior of $\Pi$ of simple partial fractions with poles on the boundary of $\Pi$ and with one fixed pole. Bibliography: 16 titles.

uniform approximation, simple partial fraction, unbounded domain, density of a semigroup