TY - JOUR

T1 - Smoothness of functions and rate of approximation

AU - Sil'vanovich, O. V.

AU - Shirokov, N. A.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - The present paper establishes a fact which, in the terminology adopted in the theory of approximation, is called the inverse theorem. The case in point is that if a function, continuous in a set, can be approximated at a given rate at some appropriate scale by some pool of approximating functions, then it has a well-defined smoothness. If, in addition, it is known that functions of smoothness considered can be approximated at a required rate, we obtain a constructive description of the smoothness class in terms of the rate of approximation.

AB - The present paper establishes a fact which, in the terminology adopted in the theory of approximation, is called the inverse theorem. The case in point is that if a function, continuous in a set, can be approximated at a given rate at some appropriate scale by some pool of approximating functions, then it has a well-defined smoothness. If, in addition, it is known that functions of smoothness considered can be approximated at a required rate, we obtain a constructive description of the smoothness class in terms of the rate of approximation.

UR - http://www.scopus.com/inward/record.url?scp=84859703973&partnerID=8YFLogxK

U2 - 10.3103/S1063454108040067

DO - 10.3103/S1063454108040067

M3 - Article

AN - SCOPUS:84859703973

VL - 41

SP - 318

EP - 323

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -