Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Delta. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions AE' subject to approximation are holomorphic in a larger angle containing Delta and there is no restriction on the growth of AE' at infinity. In [8], the problem was investigated for a wider class of functions AE' continuously complex differentiable on Delta, with sharper estimates on the growth of approximating entire functions, linked with the growth of AE' on Delta and the differential properties of AE' on the boundary of Delta. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].