Embedding and Approximation Theories in the Context of Computational (Numerical) Diameter andInternal Problems of the Theory of Functions

Abstract

The Computational (numerical) diameter, as we see it, is quite distinctly at the level "For all times!" formulates the main tasks of the Approximation Theory, Computational Mathematics and Numerical Analysis with theaccompanying computer service maintenance. Moreover, already at the task formulation stage, the corresponding unim-provable theorems of the theory of embeddings are among the first requirements for the correctness of the statement. Atthe same time, as P.L. Ulyanov claimed, that "internal problems" were in the Embedding Theorems and ApproximationTheory. This article is devoted to this.