Abstract

The approximation-theory problem to describe classes of functions in terms of the rate of approximation of these functions by polynomials, rational functions, and splines arose over 100 years ago; it still remains topical. Among many problems related to approximation, we consider the two-variable polynomial approximation problem for a function defined on the continuum of an elliptic curve in \({{\mathbb{C}}^{2}}\) and holomorphic in its interior. The formulation of such a problem leads to the need to study the approximation of functions continuous on the continuum of the complex plane and analytic in its interior, using polynomials of Weierstrass doubly periodic functions and their derivatives.This work is devoted to the development of this area.

中文翻译：

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Weierstrass双周期函数多项式逼近

摘要

根据多项式、有理函数和样条函数对这些函数的逼近率来描述函数类的逼近理论问题出现在 100 多年前；它仍然是热门话题。在许多与逼近相关的问题中，我们考虑在\({{\mathbb{C}}^{2}}\) 的椭圆曲线的连续统上定义的函数的二元多项式逼近问题，并且其内部是全纯的. 此类问题的表述导致需要使用 Weierstrass 双周期函数及其导数的多项式来研究在复平面的连续体上连续且在其内部解析的函数的逼近。这项工作致力于开发此区域。