Best weighted approximation of some kernels on the real axis

Abstract

We calculate the exact value and find the polynomial of the best weighted polynomial approximation of kernels of the form $\frac {A+Bt}{(t^2+\lambda^2)^{s+1}}$, where $A$ and $B$ are fixed complex numbers, $\lambda>0$, $s\in {\mathbb N}$, in the mean square metric.