Kirill A. Kopotun

collaborators

5 papers

math.CA2023

Onesided, intertwining, positive and copositive polynomial approximation with interpolatory constraints

German Dzyubenko, Kirill A. Kopotun

Given $k \in N$ , a nonnegative function $f \in C^{r} [a, b]$ , $r \geq 0$ , an arbitrary finite collection of points ${α_{i}}_{i \in J} \subset [a, b]$ , and a corresponding collection…

math.CA2014

Polynomial approximation with doubling weights having finitely many zeros and singularities

Kirill A. Kopotun

We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights $w$ having finitely many zeros and singularities (i.e., points where $w…

math.CA2014

New moduli of smoothness: weighted DT moduli revisited and applied

K. A. Kopotun, D. Leviatan, I. A. Shevchuk

We introduce new moduli of smoothness for functions $f \in L_{p} [- 1, 1] \cap C^{r - 1} (- 1, 1)$ , $1 \leq p \leq \infty$ , $r \geq 1$ , that have an $(r - 1)$ st locally absolutely continuous derivative…

math.CA2014

Weighted moduli of smoothness of $k$ -monotone functions and applications

Kirill A. Kopotun

Let $ω_{φ}^{k} (f, δ)_{w, L_{q}}$ be the Ditzian-Totik modulus with weight $w$ , $M^{k}$ be the cone of $k$ -monotone functions on $(- 1, 1)$ , i.e., those functions whose $k$ th divided difference…

math.CA2014

Polynomial approximation with doubling weights

Kirill A. Kopotun

Among other things, we prove that, for a doubling weight $w$ , $0 < p \leq \infty$ , $r \in N_{0}$ , and $0 < α < r + 1 - 1/ λ_{p}$ , we have \[ E_n(f)_{p, w_n} = O(n^{-α}) \iff ω_φ^{r+1}(f,…

Onesided, intertwining, positive and copositive polynomial approximation with interpolatory constraints

Polynomial approximation with doubling weights having finitely many zeros and singularities

New moduli of smoothness: weighted DT moduli revisited and applied

Weighted moduli of smoothness of k-monotone functions and applications

Polynomial approximation with doubling weights

Weighted moduli of smoothness of $k$ -monotone functions and applications