On representation of continuous functions as sums of quasianalytical ones.
type: Item
instance of: scholarly article
title: On representation of continuous functions as sums of quasianalytical ones.
zbMATH Open document ID: 1049.30500
published in: Moscow University Mathematics Bulletin
publication date: 1998-01-25T00:00:00Z
review text: In the paper the Bernstein problem is treated [see \textit{S.~Bernstein}, Collected works. Vol. 1 (1952; Zbl 0047.07301)] on the identity of two functions on \(J\). Let some set \(A\) be given in space \(C(J)\) of all functions \(f\) continuous on the segment \(J\). For two classes of functions \(B_1\) and \(B_2\) quasilinear by Bernstein on \(J\) such that every function from \(A\) is representable as \(f= f_1 + f_2\), where \(f_1\in B_1\) and \(f_2\in B_2\) it is necessary and sufficient that \(A\) be represented as a unification of some sequence of completely bounded sets from \(C(J)\).
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 30G30
zbMATH DE Number: 1109177
zbMATH Keywords: Bernstein problem
zbMATH Keywords: quasianalytical functions
author: A. V. Pokrovskiĭ
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1109177