On the best polynomial approximation in some Banach spaces for functions analytical in the unit disk
The paper is devoted to the characterization of some Banach space defined as a subspace of the Hardy space of functions analytic in the unit disk. The relation between the so-called finite order (in the present paper the case of order 0 is considered), finite type and logarithmic order of functions under consideration and, on the other side, the characteristics of the best polynomial approximation of an entire transcendental function are established. In the same way this characterizes the best approximation of the above entire functions.
scientific article; zbMATH DE number 771965
scientific article