8 citations · 30 across the 19 of their papers we have counts for
23 papers
Sharp Bernstein--Nikolskii inequalities for polynomials and entire functions of exponential type
D. V. Gorbachev
We survey Bernstein--Nikolskii inequalities for polynomials and entire functions of exponential type, with particular emphasis on sharp constants and extremal functions. We discuss…
Exact Asymptotics of the Multidimensional Nikolskii Constant
D. V. Gorbachev
We prove the exact asymptotics of the multidimensional normalized Nikolskii constant \[ \mathcal L^*(d)=\Bigl(\fracπ{2}+o(1)\Bigr)2^{-d}, \quad d\to\infty. \] In addition, fo…
The Nikolskii Constant in Arbitrary Dimension
D. V. Gorbachev
We study the radial extremal function arising in the problem of finding the sharp Nikolskii constant in for arbitra…
The Nikolskii constant in odd dimensions
D. V. Gorbachev
Let be the radial extremal function in the problem for the sharp Nikolskii constant over functions $f\in\mathit{PW}\,_{1}^…
A Bernstein--Ganzburg limit theorem for best weighted approximation
D. V. Gorbachev
We prove a Bernstein--Ganzburg type limit relation \[ \lim_{n\to\infty} \Bigl(\frac{n}σ\Bigr)^{(2a+1)/p}E_{n,σ}(f)_{p,a,b} =A_σ(f)_{p,a}, \] where is the error…
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 on the interval $[0,q]_{\scriptscriptstyle\mathbb{Z}}=[0,q…