Benjamin Scharf

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In Chapter 4 of [28] Triebel proved two theorems concerning pointwise multipliers and diffeomorphisms in function spaces Bp,q(R n) and Fs p,q(R n). 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(More)
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 this general(More)
[1] S. Dahlke, L. Diening, C. Hartmann, B. Scharf, and M. Weimar. Besov regularity of solutions to the p-Poisson equation. Preprint 2014-07, Philipps-Universität Marburg, 2014. [2] R. DeVore. Nonlinear approximation. Acta Numer., 7:51–150, 1998. [3] E. Lindgren and P. Lindqvist. Regularity of the p-Poisson equation in the plane. Technical Report 13,(More)
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 group of(More)
The rst part of this diploma thesis deals with the topic of nding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces Bs p,q(E) and F s p,q(E). We will deduce general criteria by transferring and extending a theorem of Bui, Paluszy«ski and Taibleson from the scalar to the vector-valued case. By using special norms and(More)
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, he had(More)
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