Jürgen Prestin
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Jürgen Prestin has a total of 92 co-authors. Here are the top co-authors by number of shared publications:
- Yurii Kolomoitsev
Institute for Numerical and Applied Mathematics, Göttingen University, Göttingen, Germany
7 shared publications - Elena Alexandrovna Lebedeva
Saint Petersburg State University
4 shared publications - Hrushikesh N. Mhaskar
Calif State Univ Los Angeles, Dept Math, Los Angeles, CA 90032 USA
4 shared publications - Rashad Mudhish Asharabi
Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia
4 shared publications - Ronny Bergmann
Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
4 shared publications - Daniel Potts
Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
3 shared publications
Latest Publications
- 1 February 2024
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 74 (1) , 143-150
Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
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 and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
- 1 February 2024
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 74 (1) , 143-150
Decomposition in direct sum of seminormed vector spaces and Mazur–Ulam theorem
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 and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
- Open Access
Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem
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 and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
Open AccessDecompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem
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 and sufficient conditions under which distance-preserving mappings between seminormed real vector spaces are linear.
- Open Access
- 9 March 2023
- Published by National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka) (Publications) in Reports of the National Academy of Sciences of Ukraine
- No. 1,p. 10-15
Bernstein-type characterization of entire functions
Let ε be the set of all entire functions on the complex plane C. Let us consider the class XE of all complex Banach spaces X such that X ⊇ ε . For (X, ⎥⎥ ⋅ ⎥⎥)∈XE and g ∈X we write En, X (g ) = inf {⎥⎥ g − p⎥⎥: p∈Πn }, where Πn is the set of all polynomials with degree at most n. We describe all X ∈XE for which the relation lim n→∞ (En, X( g ))1/n = 0 holds if and only if g ∈ ε.
- 9 March 2023
- Published by National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka) (Publications) in Reports of the National Academy of Sciences of Ukraine
- No. 1,p. 10-15
Open AccessBernstein-type characterization of entire functions
Let ε be the set of all entire functions on the complex plane C. Let us consider the class XE of all complex Banach spaces X such that X ⊇ ε . For (X, ⎥⎥ ⋅ ⎥⎥)∈XE and g ∈X we write En, X (g ) = inf {⎥⎥ g − p⎥⎥: p∈Πn }, where Πn is the set of all polynomials with degree at most n. We describe all X ∈XE for which the relation lim n→∞ (En, X( g ))1/n = 0 holds if and only if g ∈ ε.
- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Foundations of Computing
- Vol. 6 (1) , 14-40
Analysis of directional higher order jump discontinuities with trigonometric shearlets
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 extend these results to bivariate periodic functions which have jump discontinuities in higher order directional derivatives along edges. In order to prove suitable upper and lower bounds for the shearlet coefficients, we need to generalize the results about localization- and orientation-dependent decay properties of the corresponding inner products of trigonometric shearlets and the underlying periodic functions.
- 1 January 2023
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Foundations of Computing
- Vol. 6 (1) , 14-40
Analysis of directional higher order jump discontinuities with trigonometric shearlets
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 extend these results to bivariate periodic functions which have jump discontinuities in higher order directional derivatives along edges. In order to prove suitable upper and lower bounds for the shearlet coefficients, we need to generalize the results about localization- and orientation-dependent decay properties of the corresponding inner products of trigonometric shearlets and the underlying periodic functions.
- Open Access
Approximation properties of periodic multivariate quasi-interpolation operators
We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetilde{\varphi}_j$ and trigonometric polynomials $\varphi_j$. The class of such operators includes classical interpolation polynomials ($\widetilde\varphi_j$ is the Dirac delta function), Kantorovich-type operators ($\widetilde\varphi_j$ is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on $\widetilde\varphi_j$ and $\varphi_j$, we obtain upper and lower bound estimates for the $L_p$-error of approximation by quasi-interpolation operators in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, $K$-functionals, and other terms.Open AccessApproximation properties of periodic multivariate quasi-interpolation operators
We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetilde{\varphi}_j$ and trigonometric polynomials $\varphi_j$. The class of such operators includes classical interpolation polynomials ($\widetilde\varphi_j$ is the Dirac delta function), Kantorovich-type operators ($\widetilde\varphi_j$ is a characteristic function), scaling expansions associated with wavelet constructions, and others. Under different compatibility conditions on $\widetilde\varphi_j$ and $\varphi_j$, we obtain upper and lower bound estimates for the $L_p$-error of approximation by quasi-interpolation operators in terms of the best and best one-sided approximation, classical and fractional moduli of smoothness, $K$-functionals, and other terms. - 6 June 2021
- Published by Springer Nature
- p. 267-335
Funktionen
- Open Access
- 1 March 2021
- Published by Walter de Gruyter GmbH in Mitteilungen der Deutschen Mathematiker-Vereinigung
- Vol. 29 (1) , 14-21
Die 61. Internationale Mathematik-Olympiade
Article Die 61. Internationale Mathematik-Olympiade was published on March 1, 2021 in the journal Mitteilungen der Deutschen Mathematiker-Vereinigung (volume 29, issue 1).
- 1 March 2021
- Published by Walter de Gruyter GmbH in Mitteilungen der Deutschen Mathematiker-Vereinigung
- Vol. 29 (1) , 14-21
Open AccessDie 61. Internationale Mathematik-Olympiade
Article Die 61. Internationale Mathematik-Olympiade was published on March 1, 2021 in the journal Mitteilungen der Deutschen Mathematiker-Vereinigung (volume 29, issue 1).
- Open Access
- 8 February 2021
- Published by Springer Nature in Advances in Computational Mathematics
- Vol. 47 (1) , 1-41
Edge detection with trigonometric polynomial shearlets
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 step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.
- 8 February 2021
- Published by Springer Nature in Advances in Computational Mathematics
- Vol. 47 (1) , 1-41
Open AccessEdge detection with trigonometric polynomial shearlets
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 step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.
- 1 January 2021
- Published by Springer Nature
Die schönsten Aufgaben der Mathematik-Olympiade in Deutschland
- 1 January 2021
- Published by Springer Nature
Die schönsten Aufgaben der Mathematik-Olympiade in Deutschland