arXiv subjects
Publications and source records attributed to V. V. Savchuk.
We calculated the exact value and found the polynomial of the best weighted polynomial approximation of the kernels of the form $\frac {A+Bx}{(x^2+λ^2)^2}$, where $A,B\in {\mathbb R}$, $λ>0$ in the mean-square metric.
Let $φ=\{φ_k\}_{k=-\infty}^\infty$ denote the extended Takenaka--Malmquist system on unit circle $\mathbb T$ and let $σ_{n,φ}(f),$ $f\in L^1(\mathbb T)$, be the Fejér-type operator based on $φ$, introduced by V. N. Rusak. We give the convergence criteria for $σ_{n,φ}(f)$ in Banach space $X(\mathbb T):=L^p(\mathbb T)\vee C(\mathbb T)$, $p\ge 1$. Also we prove the Voronovskaya-type theorem for $σ_{n,φ}(f)$ on class of holomorphic functions representable by Cauchy-type integrals with bounded densities.