Approximation by polynomials composed of Weierstrass doubly periodic functions

The problem of describing classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, splines entered in the theory of approximation more than 100 years ago and still retains its relevance. Among a large number of problems related to approximation, we considered the problem of polynomial approximation in two variables of a function defined on the continuum of an elliptic curve in $C_2$ and holomorphic in its interior. The formulation of such a question led to the need to study the approximation of a function that is continuous on the continuum of the complex plane and analytic in its interior, using polynomials in doubly periodic Weierstrass functions and their derivatives. This work is devoted to the development of this topic.