F. Voigtlaender

activity

20142026

most citedOn the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel

16 citations · 69 across the 34 of their papers we have counts for

collaborators

Showing math.FAShow all

31 papers · 1 filter

math.FA2026

Maximally Spread Out Measures and Implications for Phase Transitions in Approximation Theory

Hannes Matt, Erwin Riegler, Felix Voigtlaender

We establish the existence of a "maximally spread out" Borel probability measure on a totally bounded subset $\SC$ of a (…

math.FA2026

Linear dependence of time-frequency shifts of a Schwartz function

Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven +1

We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwal…

math.FA2024

Smoothness spaces for warped time-frequency representations -- Decomposition spaces and embedding relations

Nicki Holighaus, Felix Voigtlaender

In a recent paper, we have shown that warped time-frequency representations provide a rich framework for the construction and study of smoothness spaces matched to very general pha…

math.FA2023★ 3 cited

Optimal approximation using complex-valued neural networks

Paul Geuchen, Felix Voigtlaender

Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the…

math.FA2022

Classification of anisotropic Triebel-Lizorkin spaces

Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender

This paper provides a classification theorem for expansive matrices $A \in GL (d, R)$ generating the same anisotropic homogeneous Triebel-Lizorkin space $\dot{\mat…

math.FA2022

$L^{p}$ sampling numbers for the Fourier-analytic Barron space

Felix Voigtlaender

In this paper, we consider Barron functions $f : [0, 1]^{d} \to R$ of smoothness $σ > 0$ , which are functions that can be written as \[ f(x) = \int_{\mathbb{R}^d} F(ξ) \, e^{2…

math.FA2022

Coorbit theory of warped time-frequency systems in $R^{d}$

Nicki Holighaus, Felix Voigtlaender

Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the s…

math.FA2022

Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II

Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender

Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces $F ˙_{p, q}^{α}$ for the endpoint case of $p = \infty$ and…

math.FA2022

Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition

Jordy Timo van Velthoven, Felix Voigtlaender

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and…

math.FA2021★ 4 cited

Optimal learning of high-dimensional classification problems using deep neural networks

Philipp Petersen, Felix Voigtlaender

We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish…

math.FA2021

Sobolev-type embeddings for neural network approximation spaces

Philipp Grohs, Felix Voigtlaender

We consider neural network approximation spaces that classify functions according to the rate at which they can be approximated (with error measured in $L^{p}$ ) by ReLU neural networ…

math.FA2021

A note on the invertibility of the Gabor frame operator on certain modulation spaces

Dae Gwan Lee, Friedrich Philipp, Felix Voigtlaender

We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space $V_{1} = H^{1} (R^{d})$ , the weighted…

math.FA2021

Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I

Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender

This paper provides maximal function characterizations of anisotropic Triebel-Lizorkin spaces associated to general expansive matrices for the full range of parameters $p \in (0,\i…

math.FA2020★ 3 cited

The universal approximation theorem for complex-valued neural networks

Felix Voigtlaender

We generalize the classical universal approximation theorem for neural networks to the case of complex-valued neural networks. Precisely, we consider feedforward networks with a co…

math.FA2020★ 7 cited

Neural network approximation and estimation of classifiers with classification boundary in a Barron class

Andrei Caragea, Philipp Petersen, Felix Voigtlaender

We prove bounds for the approximation and estimation of certain binary classification functions using ReLU neural networks. Our estimation bounds provide a priori performance guara…

math.FA2020

Phase Transitions in Rate Distortion Theory and Deep Learning

Philipp Grohs, Andreas Klotz, Felix Voigtlaender

Rate distortion theory is concerned with optimally encoding a given signal class $S$ using a budget of $R$ bits, as $R \to \infty$ . We say that $S$ can be compres…

math.FA2020

Schur-type Banach modules of integral kernels acting on mixed-norm Lebesgue spaces

Nicki Holighaus, Felix Voigtlaender

Schur's test states that if $K : X \times Y \to C$ satisfies $\int_{Y} ∣ K (x, y) ∣ d ν (y) \leq C$ and $\int_{X} ∣ K (x, y) ∣ d μ (x) \leq C$ , then the associated integral operator acts boundedly…

math.FA2020

On dual molecules and convolution-dominated operators

José Luis Romero, Jordy Timo van Velthoven, Felix Voigtlaender

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the siz…

math.FA2019

Invertibility of frame operators on Besov-type decomposition spaces

José Luis Romero, Jordy Timo van Velthoven, Felix Voigtlaender

We derive an extension of the Walnut-Daubechies criterion for the invertibility of frame operators. The criterion concerns general reproducing systems and Besov-type spaces. As an…

math.FA2019

Design and properties of wave packet smoothness spaces

Dimitri Bytchenkoff, Felix Voigtlaender

We introduce a family of quasi-Banach spaces - which we call wave packet smoothness spaces - that includes those function spaces which can be characterised by the sparsity of their…

math.FA2019★ 1 cited

Approximation in $L^{p} (μ)$ with deep ReLU neural networks

Felix Voigtlaender, Philipp Petersen

We discuss the expressive power of neural networks which use the non-smooth ReLU activation function $ϱ (x) = max {0, x}$ by analyzing the approximation theoretic properties…

math.FA2019★ 1 cited

Time-Frequency Shift Invariance of Gabor Spaces with an $S_{0}$ -Generator

Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1

We consider Gabor Riesz sequences generated by a lattice $Λ \subset R^{2}$ and a window function $g \in L^{2} (R)$ which is well localized in both time and frequency. W…

math.FA2019

A quantitative subspace Balian-Low theorem

Andrei Caragea, Dae Gwan Lee, Friedrich Philipp +1

Let $G \subset L^{2} (R)$ be the subspace spanned by a Gabor Riesz sequence $(g, Λ)$ with $g \in L^{2} (R)$ and a lattice $Λ \subset R^{2}$ of rational density.…

math.FA2018★ 16 cited

On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel

Stephan Dahlke, Filippo De Mari, Ernesto De Vito +4

This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of…

Maximally Spread Out Measures and Implications for Phase Transitions in Approximation Theory

Linear dependence of time-frequency shifts of a Schwartz function

Smoothness spaces for warped time-frequency representations -- Decomposition spaces and embedding relations

Optimal approximation using complex-valued neural networks

Classification of anisotropic Triebel-Lizorkin spaces

Lp sampling numbers for the Fourier-analytic Barron space

Coorbit theory of warped time-frequency systems in Rd

Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II

Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition

Optimal learning of high-dimensional classification problems using deep neural networks

Sobolev-type embeddings for neural network approximation spaces

A note on the invertibility of the Gabor frame operator on certain modulation spaces

Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I

The universal approximation theorem for complex-valued neural networks

Neural network approximation and estimation of classifiers with classification boundary in a Barron class

Phase Transitions in Rate Distortion Theory and Deep Learning

Schur-type Banach modules of integral kernels acting on mixed-norm Lebesgue spaces

On dual molecules and convolution-dominated operators

Invertibility of frame operators on Besov-type decomposition spaces

Design and properties of wave packet smoothness spaces

Approximation in Lp(μ) with deep ReLU neural networks

Time-Frequency Shift Invariance of Gabor Spaces with an S0​-Generator

A quantitative subspace Balian-Low theorem

On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel

$L^{p}$ sampling numbers for the Fourier-analytic Barron space

Coorbit theory of warped time-frequency systems in $R^{d}$

Approximation in $L^{p} (μ)$ with deep ReLU neural networks

Time-Frequency Shift Invariance of Gabor Spaces with an $S_{0}$ -Generator