On representation of continuous functions as sums of quasianalytical ones.
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 \(C(J)\).
scientific article; zbMATH DE number 1109177