Applied Functional Analysis group

TU Berlin

Email: felix@voigtlaender.xyz

CV (last updated on 23 September 2017)

- Function spaces and their embeddings
- Multiscale systems (wavelets, shearlets and generalizations)
- Banach frames and atomic decompositions
- Approximation theory, in particular the approximation properties of multiscale systems
- Coorbit theory
- Time-frequency analysis
- Fourier analysis

I am a Postdoctoral researcher in the Applied Functional Analysis group at TU Berlin, part of the group of Gitta Kutyniok.

I studied mathematics (Bachelor + Master) and computer science (Bachelor) at RWTH Aachen University, Germany, where I graduated with the Master degree with distinction in 2013.

As a Ph.D. student, I then joined the group of Hartmut Führ at RWTH Aachen University, where I studied the approximation theoretic properties of different multiscale systems.
With my Ph.D. thesis *'Embedding Theorems for Decomposition Spaces with applications to Wavelet Coorbit Spaces'*, I graduated with distinction in November 2015.
In November 2016, I was awarded the Friedrich-Wilhelm-Award 2016
for my thesis.

I highly enjoy teaching mathematics and am committed to explaining carefully and presenting the material in an enjoyable way. At RWTH Aachen University, I have been teaching assistant for Analysis I and III, and for Harmonic analysis. Therefore, I am very proud to have received the Teaching award of the student council of mathematics at RWTH Aachen University.

Since April 2016 I am a postdoctoral researcher at TU Berlin, where I am working on the DEDALE project.

After my talk about the approximation properties of ReLU neural networks at the Research seminar "Mathematics of Computation", I was asked for the slides to my talk. These can be found here.

Many thanks to Tino Ullrich for inviting me to give this talk!

I just added to my list of publications two new preprints that I recently uploaded to the arXiv.

The first one establishes a rather general version of Price's theorem: It gives a simple formula for computing the partial derivatives of the map ρ ↦ 𝔼[g(Xᵨ)], where Xᵨ is a normally distributed random variable with covariance matrix ρ. Price published this result in 1958, but did not precisely state the required assumptions on g. In the paper, I show that one can in fact take every tempered distribution g. This result is used in the paper ℓ¹-Analysis Minimization and Generalized (Co-)Sparsity: When Does Recovery Succeed? written by three of my colleagues.

The second preprint, written jointly with my colleague Philipp Petersen analyzes the approximation power of neural networks that use the ReLU activation function. We analyze how deep and wide such a neural network needs to be, in order to approximate any "piecewise smooth" function. We also show that these bounds are sharp.

I also added several talks that I gave in the last months, including the lecture notes for the lecture series "Sparsity Properties of Frames via Decomposition Spaces" that I gave at the Summer School on Applied Harmonic Analysis in Genoa.

I just added a new preprint to my list of publications that I uploaded to the arXiv in December.

Furthermore, I am *very* happy to be a speaker at the Summer School on Applied Harmonic Analysis that will take place in Genoa from July 24-28, 2017.

Finally, I want to mention that my toy problem (about whether completeness of spaces can be characterized by the convergence of Neumann series) has been solved (negatively) quite a while ago.

First version of this website was uploaded :)