Zobrazeno 1 - 10
of 109
pro vyhledávání: '"Andrievskii, Vladimir"'
Autor:
Andrievskii, Vladimir, Nazarov, Fedor
Let $K\subset \mathbb R$ be a regular compact set and let $g(z)=g_{\overline{\mathbb C}\setminus K}(z,\infty)$ be the Green function for $\overline{\mathbb C}\setminus K$ with pole at infinity. For $\delta>0$, define $$ G(\delta):=\max\{ g(z): z\in \
Externí odkaz:
http://arxiv.org/abs/2111.04607
Autor:
Andrievskii, Vladimir
We prove an analogue of the classical Bernstein polynomial inequality on a compact subset $E$ of the real line. The Lipschitz continuity of the Green function for the complement of $E$ with respect to the extended complex plane and the differentiabil
Externí odkaz:
http://arxiv.org/abs/1811.12863
Autor:
Andrievskii, Vladimir
Let $K$ be a compact set in the complex plane consisting of a finite number of continua. We study the rate of approximation of $K$ from the outside by lemniscates in terms of level lines of the Green function for the complement of $K$.
Externí odkaz:
http://arxiv.org/abs/1805.10932
Autor:
Andrievskii, Vladimir
We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.
Externí odkaz:
http://arxiv.org/abs/1712.07054
Autor:
Andrievskii, Vladimir, Nazarov, Fedor
Publikováno v:
In Journal of Approximation Theory March 2022 275
Autor:
Andrievskii, Vladimir
We establish sharp $L_p,1\le p<\infty$ weighted Remez- and Nikolskii-type inequalities for algebraic polynomials considered on a quasismooth (in the sense of Lavrentiev) curve in the complex plane.
Externí odkaz:
http://arxiv.org/abs/1707.06976
Autor:
Andrievskii, Vladimir
The estimates of the uniform norm of the Chebyshev polynomials associated with a compact set $K$ in the complex plane are established. These estimates are exact (up to a constant factor) in the case where $K$ consists of a finite number of quasiconfo
Externí odkaz:
http://arxiv.org/abs/1701.06202
Autor:
Andrievskii, Vladimir
Using the theory of quasiconformal mappings, we simplify the proof of the recent result by Taylor and Totik (see IMA Journal of Numerical Analysis 30 (2010) 462--486) on the behavior of the Lebesgue constants for interpolation points on a compact set
Externí odkaz:
http://arxiv.org/abs/1612.00519
Autor:
Andrievskii, Vladimir
We establish the exact (up to the constants) double inequality for the Christoffel function for a measure supported on a Jordan domain bounded by a quasiconformal curve. We show that this quasiconformality of the boundary cannot be omitted.
Externí odkaz:
http://arxiv.org/abs/1612.00517