# Benjamin ScharfTechnische Universität München | TUM · Faculty of Mathematics

Benjamin Scharf

Postdoc (Dr. rer. nat)

## About

9

Publications

737

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114

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

## Publications

Publications (9)

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...

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...

In Chapter 4 of 28 Triebel proved two theorems concerning pointwise multipliers and diffeomorphisms in function spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$B^s_{p,q}(\mathbb {R}^n)$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$F^{s}_{p,q}(\mathbb {R}^n)$\end{d...

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,...

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...

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...

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,...

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.

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...