Optimal Uniform and Tangential Approximation in an Angle by Meromorphic Functions

摘要

For functions that are holomorphic on the interior of given angle and continuous in the angle, we discuss the problem of uniform and tangential approximation in the angle by meromorphic functions having optimal growth at infinity. We show that this growth depends on the growth of underlying function in the angle and the differential properties on the boundary of the angle. We estimate the growth of the function by its Nevanlinna characteristic. Also, we consider a question of description of the possible set of the poles of the approximating functions on the complex plane.