Benjamin Scharf

Benjamin Scharf
Technische Universität München | TUM · Faculty of Mathematics

Postdoc (Dr. rer. nat)

About

9
Publications
629
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94
Citations
Introduction
I started to work as a doctoral student in the research group function spaces under the supervision of Hans Triebel and Hans-Jürgen Schmeißer. After my PhD I moved to TU Munich at the chair of Applied Numerical Analysis under head Massimo Fornasier working with Besov Regularity and Sparse Control of Dynamical systems right now.
Additional affiliations
June 2009 - February 2013
Friedrich Schiller University Jena
Position
  • PhD Student

Publications

Publications (9)
Article
Full-text available
For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct low-dimensional representations of the dynamical system, which allow the learning of nearly optimal control strategies in high dimension with overwhelming confidence. In this paper we present an instance of thi...
Article
Full-text available
In this paper, we study the regularity of solutions to the $p$-Poisson equation for all $1<p<\infty$. In particular, we are interested in smoothness estimates in the adaptivity scale $ B^\sigma_{\tau}(L_{\tau}(\Omega))$, $1/\tau = \sigma/d+1/p$, of Besov spaces. The regularity in this scale determines the order of approximation that can be achieved...
Article
In Chapter 4 of 28 Triebel proved two theorems concerning pointwise multipliers and diffeomorphisms in function spaces and . In each case he presented two approaches, one via atoms and one via local means. While the approach via atoms was very satisfactory concerning the length and simplicity, only the rather technical approach via local means prov...
Article
A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel–Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases in function spaces of Besov and Triebel–Lizorkin type on cellular domains, in particular on the cube. However,...
Article
Full-text available
Nowadays the theory and application of wavelet decompositions plays an important role not only for the study of function spaces (of Lebesgue, Hardy, Sobolev, Besov, Triebel-Lizorkin type) but also for its applications in signal and numerical analysis, partial differential equations and image processing. In this context it it a hard problem to const...
Article
Full-text available
Collective migration of animals in a cohesive group is rendered possible by a strategic distribution of tasks among members: some track the travel route, which is time and energy-consuming, while the others follow the group by interacting among themselves. In this paper, we study a social dynamics system modeling collective migration. We consider a...
Article
A rather tricky question is the construction of wavelet bases on domains for suitable function spaces (Sobolev, Besov, Triebel-Lizorkin type). In his monograph from 2008, Triebel presented an approach how to construct wavelet (Riesz) bases in function spaces of Besov and Triebel-Lizorkin type on cellular domains, in particular on the cube. However,...
Article
We characterize the traces of vector-valued Besov and Lizorkin-Triebel spaces. Therefrom we derive the corresponding assertions for the vector-valued Sobolev spaces . Here we do not assume the UMD property for the Banach space E.
Article
Full-text available
The first part of this paper deals with the topic of finding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces. We will deduce general criteria by transferring and extending a theorem of Bui, Paluszynski and Taibleson from the scalar to the vector-valued case. By using special norms and characterizations we...

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