On best nonsymmetric $L_1$-approximations of some classes of convolutions with generalized splines

Abstract

We obtain the exact values of the best non-symmetric approximations of the classes of convolutions with $CVD$-kernels by splines $S_{2n,K_1}$ and $S_{2n,K_2}^{1}$ such that $ \bigvee _{0}^{2 \pi} \left( s \right) \le 1$ and $ \| s \| \ _{1} \le 1 $ respectively.