11 citations · 29 across the 16 of their papers we have counts for
19 papers
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…
Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem
Oleksiy Dovgoshey, Jürgen Prestin, Igor Shevchuk
It was proved by S. Mazur and S. Ulam in 1932 that every isometric surjection between normed real vector spaces is affine. We generalize the Mazur--Ulam theorem and find necessary…
Analysis of directional higher order jump discontinuities with trigonometric shearlets
Kevin Schober, Jürgen Prestin
In a recent article, we showed that trigonometric shearlets are able to detect directional step discontinuities along edges of periodic characteristic functions. In this paper, we…
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…
Edge detection with trigonometric polynomial shearlets
Jürgen Prestin, Kevin Schober, Serhii A. Stasyuk
In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin type wavelets are able to detect singularities alo…
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…
Directional Heisenberg uncertainty product
A. Krivoshein, E. Lebedeva, E. Neiman +1
A directional time-frequency localization measure for functions defined on the -dimensional Euclidean space is introduced. A connection between this measure and its periodic cou…
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…
Translation matrix elements for spherical Gauss-Laguerre basis functions
Jürgen Prestin, Christian Wülker
Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type , , cons…
A directional uncertainty principle for periodic functions
A. Krivoshein, E. Lebedeva, J. Prestin
In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction.…
Smoothing of weights in the Bernstein approximation problem
Andrew Bakan, Jürgen Prestin
In 1924 S.Bernstein asked for conditions on a uniformly bounded on Borel function (weight) which imply the denseness of algebraic pol…
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.
Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions
Jürgen Prestin, Christian Wülker
Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type , , $L_…
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…