11 citations · 29 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
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…