6 papers
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…
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…
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…