Uniform and tangential approximation in a stripe by meromorphic functions of optimal growth

The paper discusses the problem of approximation of functions continuous on a closed stripe S _h = {z: |Imz| ≤h} and holomorphic in its interior. The results relate to the uniform and tangential approximation of such functions f by meromorphic functions g with minimal growth in terms of Nevanlinna characteristic T (r, g). The growth depends on the growth of f in S _h and certain differential properties of f on ?S _h . It is assumed that the possible poles of g are restricted to the imaginary axis.