Optimally uniform approximation by meromorphic functions in the strip

The paper studies the uniform approximation problem of functions f, which are continuous in a closed strip S _h and holomorphic in its interior. Such functions are approximated on S _h by meromorphic functions g, the growth of which is estimated in the terms of the Nevanlinna characteristic T (r, g) and depends on the growth of f in the strip and the differential properties of f on the boundary of the strip. Also, the possible location of the poles of g in the complex plane is studied.