On the representation by sums of algebras of continuous functions

被引：2

作者：

Asgarova, Aida Kh. ^{[1
]}

Ismailov, Vugar E. ^{[1
]}

机构：

[1] Natl Acad Sci Azerbaijan, Inst Math & Mech, AZ-1141 Baku, Azerbaijan

来源：

COMPTES RENDUS MATHEMATIQUE | 2017年 / 355卷 / 09期

关键词：

RIDGE FUNCTIONS; GOOD SETS; LINEAR SUPERPOSITIONS; APPROXIMATION; INTERPOLATION; VARIABLES; PRODUCT;

D O I：

10.1016/j.crma.2017.09.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a necessary condition for the representation of the space of continuous functions by sums of its k closed subalgebras. A sufficient condition for this representation problem was first obtained by Sternfeld in 1978. In case of two subalgebras (k = 2), our necessary condition turns out to be also sufficient. If k = 1, our result coincides with a version of the classical Stone-Weierstrass theorem. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：949 / 955

页数：7

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