D. Gorbachev

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math.CA2026

The Nikolskii Constant in Arbitrary Dimension

D. V. Gorbachev

We study the radial extremal function $φ (∣ \cdot ∣)$ arising in the problem of finding the sharp Nikolskii constant $C_{d}$ in $PW_{1}^{1} (R^{d})$ for arbitra…

math.CA2026

A Bernstein--Ganzburg limit theorem for best weighted approximation

D. V. Gorbachev

We prove a Bernstein--Ganzburg type limit relation \[ \lim_{n\to\infty} \Bigl(\frac{n}Ï\Bigr)^{(2a+1)/p}E_{n,Ï}(f)_{p,a,b} =A_Ï(f)_{p,a}, \] where $E_{n, I ¨ } (f)_{p, a, b}$ is the e…

math.CA2025

Chebyshev systems and Sturm oscillation theory for discrete polynomials

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

We prove an analogue of Chebyshev's alternation theorem for linearly independent discrete functions $Φ_{n} = {φ_{k}}_{k = 1}^{n}$ on the interval $[0,q]_{\scriptscriptstyle\mathbb{Z}}=[0,q…