11 citations · 29 across the 16 of their papers we have counts for
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Approximation on hexagonal domains by Taylor-Abel-Poisson means
Jürgen Prestin, Viktor Savchuk, Andrii Shidlich
Approximative properties of the Taylor-Abel-Poisson linear summation me\-thod of Fourier series are considered for functions of several variables, periodic with respect to the hexa…
Approximation properties of periodic multivariate quasi-interpolation operators
Yurii Kolomoitsev, Jürgen Prestin
We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions and trigonometric p…
Approximation theorems for multivariate Taylor-Abel-Poisson means
Jürgen Prestin, Viktor Savchuk, Andrii Shidlich
We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers i…
On -error of bivariate polynomial interpolation on the square
Yurii Kolomoitsev, Tetiana Lomako, Jürgen Prestin
We obtain estimates of the -error of the bivariate polynomial interpolation on the Lissajous-Chebyshev node points for wide classes of functions including non-smooth functions…
Boundedness of Lebesgue constants and interpolating Faber bases
Viktoriia Bilet, Oleksiy Dovgoshey, Jürgen Prestin
We investigate some conditions under which the Lebesgue constants or Lebesgue functions are bounded for the classical Lagrange polynomial interpolation on a compact subset of $\mat…
Direct and inverse approximation theorems of -periodic functions by Taylor--Abel--Poisson means
Jürgen Prestin, Viktor Savchuk, Andrii Shidlich
We obtain direct and inverse approximation theorems of -periodic functions by Taylor--Abel--Poisson operators in the integral metric.
On approximation of functions by algebraic polynomials in Hölder spaces
Yurii Kolomoitsev, Tetiana Lomako, Jürgen Prestin
We study approximation of functions by algebraic polynomials in the Hölder spaces corresponding to the generalized Jacobi translation and the Ditzian-Totik moduli of smoothness. By…
Recovery of periodicities hidden in heavy-tailed noise
Illya M. Karabash, Jürgen Prestin
We address a parametric joint detection-estimation problem for discrete signals of the form , , with an additive no…
Sharp estimates of approximation of periodic functions in Hölder spaces
Yurii Kolomoitsev, Jürgen Prestin
The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the Hölder spaces for all and . By using mo…
Two ideals connected with strong right upper porosity at a point
V. Bilet, O. Dovgoshey, J. Prestin
Let be the set of upper strongly porous at subsets of and let be the intersection of maximal ideals . Some characteristic prop…
Periodic wavelet frames and time-frequency localization
Elena A. Lebedeva, Jürgen Prestin
A family of Parseval periodic wavelet frames is constructed. The family has optimal time-frequency localization (in the sense of the Breitenberger uncertainty constant) with respec…