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.
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页码：949 / 955
页数：7
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