The best approximation to a class of functions of several variables by another class and related extremum problems

V. V. Arestov

Matematičeskie zametki, Tome 64 (1998) no. 3, pp. 323-340

Résumé

We study the relationship between several extremum problems for unbounded linear operators of convolution type in the spaces $L_\gamma=L_\gamma(\mathbb R^m)$, $m\ge1$, $1\le\gamma\le\infty$. For the problem of calculating the modulus of continuity of the convolution operator $A$ on the function class $Q$ defined by a similar operator and for the Stechkin problem on the best approximation of the operator $A$ on the class $Q$ by bounded linear operators, we construct dual problems in dual spaces, which are the problems on, respectively, the best and the worst approximation to a class of functions by another class.