4 papers
Estimates of Lebesgue Constants for Lagrange Interpolation Processes by Rational Functions under Mild Restrictions to their Fixed Poles
Sergei Kalmykov, Alexey Lukashov
We estimate the Lebesgue constants for Lagrange interpolation processes on one or several intervals by rational functions with fixed poles. We admit that the poles have accumulatio…
Loewner Evolution as Itô Diffusion
Hülya Acar, Alexey L. Lukashov
F. Bracci, M.D. Contreras, S. Díaz Madrigal proved that any evolution family of order d is described by a generalized Loewner chain. G. Ivanov and A. Vasil'ev considered randomized…
The order of Lebesgue constant of Lagrange interpolation on several intervals
A. L. Lukashov, J. Szabados
We consider Lagrange interpolation on the set of finitely many intervals. This problem is closely related to the least deviating polynomial from zero on such sets. We will obtain l…
Approximation of sgn(x) on two symmetric intervals by rational functions with fixed poles
A. Lukashov, D. Prokhorov
Recently A. Eremenko and P. Yuditskii found explicit solutions of the best polynomial approximation problems of sgn(x) over two intervals in terms of conformal mappings onto specia…