On the Theorem of 𝑀 Golomb

Proceedings Mathematical Sciences

Vugar E Ismailov¹ 

[1] Mathematics and Mechanics Institute, Azerbaijan National Academy of Sciences, Az-, Baku, Azerbaijan$$

关键词: Approximation error;    duality relation;    projection cycle;    lightning bolt;    orthogonal measure;    extreme measure.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $X_1,ldots,X_n$ be compact spaces and $X=X_1×cdots× X_n$. Consider the approximation of a function $fin C(X)$ by sums $g_1(x_1)+cdots+g_n(x_n)$, where $g_iin C(X_i),i=1,ldots,n$. In [8], Golomb obtained a formula for the error of this approximation in terms of measures constructed on special points of 𝑋, called `projection cycles’. However, his proof had a gap, which was pointed out by Marshall and O’Farrell [15]. But the question if the formula was correct, remained open. The purpose of the paper is to prove that Golomb’s formula holds in a stronger form.

【 授权许可】

Unknown