Journal articles and (machine learning) conference proceedings

• Optimal approximation using complex-valued neural networks
  P. Geuchen and F. Voigtlaender
  NeurIPS 2023 (Poster)

• Sampling numbers of smoothness classes via ℓ¹-minimization
  T. Jahn, T. Ullrich, and F. Voigtlaender
  Journal of Complexity; doi: 10.1016/j.jco.2023.101786

• Learning ReLU networks to high uniform accuracy is intractable
  J. Berner, P. Grohs, and F. Voigtlaender
  ICLR 2023 (Poster)

• Classification of anisotropic Triebel-Lizorkin spaces
  S. Koppensteiner, J. T. van Velthoven and F. Voigtlaender
  Mathematische Annalen; doi: 10.1007/s00208-023-02690-y

• Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II
  S. Koppensteiner, J. T. van Velthoven, and F. Voigtlaender
  Monatshefte für Mathematik; doi: 10.1007/s00605-023-01824-3

• Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I
  S. Koppensteiner, J. T. van Velthoven, and F. Voigtlaender
  Monatshefte für Mathematik; doi: 10.1007/s00605-023-01827-0

• Sobolev-type embeddings for neural network approximation spaces
  P. Grohs and F. Voigtlaender
  Constructive Approximation; doi: 10.1007/s00365-022-09598-x

• Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces
  P. Grohs and F. Voigtlaender
  Foundations of Computational Mathematics; doi: 10.1007/s10208-023-09607-w

• The universal approximation theorem for complex-valued neural networks
  F. Voigtlaender
  Applied and Computational Harmonic Analysis; doi: 10.1016/j.acha.2022.12.002

• Neural network approximation and estimation of classifiers with classification boundary in a Barron class
  A. Caragea, P. Petersen, and F. Voigtlaender
  Annals of Applied Probability; doi: 10.1214/22-AAP1884

• A Balian–Low type theorem for Gabor Riesz sequences of arbitrary density
  A. Caragea, D.G. Lee, F. Philipp, and F. Voigtlaender
  Mathematische Zeitschrift; doi: 10.1007/s00209-022-03182-6

• A note on the invertibility of the Gabor frame operator on certain modulation spaces
  D.G. Lee, F. Philipp, and F. Voigtlaender
  Journal of Fourier Analysis and Applications; doi: 10.1007/s00041-022-09980-0

• Structured, compactly supported Banach frame decompositions of decomposition spaces
  F. Voigtlaender
  Dissertationes Mathematicae; doi: 10.4064/dm804-5-2021

• A fractal uncertainty principle for Bergman spaces and analytic wavelets
  Luis Daniel Abreu, Zouhair Mouayn, and Felix Voigtlaender
  Journal of Mathematical Analysis and Applications; doi: 10.1016/j.jmaa.2022.126699

• Invertibility of frame operators on Besov-type decomposition spaces
  J.L. Romero, J. T. van Velthoven, and F. Voigtlaender
  Journal of Geometric Analysis (2022); doi: 10.1007/s12220-022-00887-2

• Quantitative approximation results for complex-valued neural networks
  A. Caragea, D.G. Lee, J. Maly, G. Pfander, and F. Voigtlaender
  SIAM Journal on Mathematics of Data Science (SIMODS) doi: 10.1137/21M1429540

• Phase Transitions in Rate Distortion Theory and Deep Learning
  Philipp Grohs, Andreas Klotz, and F. Voigtlaender
  Foundations of Computational Mathematics; doi: 10.1007/s10208-021-09546-4

• Schur-type Banach modules of integral kernels acting on mixed-norm Lebesgue spaces
  N. Holighaus and F. Voigtlaender
  Journal of Functional Analysis; doi: 10.1016/j.jfa.2021.109197

• A quantitative subspace Balian-Low theorem
  A. Caragea, D.G. Lee, F. Philipp, and F. Voigtlaender
  Applied and Computational Harmonic Analysis; doi: 10.1016/j.acha.2021.06.005

• On dual molecules and convolution-dominated operators
  J.L. Romero, J. T. van Velthoven, and F. Voigtlaender
  Journal of Functional Analysis; doi: 10.1016/j.jfa.2021.108963

• Negative results for approximation using single layer and multilayer feedforward neural networks
  J. M. Almira, P.E. Lopez-de-Teruel, D.J. Romero-Lopez, and F. Voigtlaender
  Journal of Mathematical Analysis and Applications 494(1):124584, 2021; doi: 10.1016/j.jmaa.2020.124584

• Approximation spaces of deep neural networks
  R. Gribonval, G. Kutyniok, M. Nielsen, and F. Voigtlaender
  Constructive Approximation; doi: 10.1007/s00365-021-09543-4

• Embeddings of Decomposition Spaces
  F. Voigtlaender
  Memoirs of the AMS doi: 10.1090/memo/1426

• A general version of Price's theorem
  F. Voigtlaender
  Journal of Theoretical Probability (2020); doi: 10.1007/s10959-020-01017-w

• Topological properties of the set of functions generated by neural networks of fixed size
  P. Petersen, M. Raslan, and F. Voigtlaender
  Foundations of Computational Mathematics (2020); doi: 10.1007/s10208-020-09461-0

• Equivalence of approximation by convolutional neural networks and fully-connected networks
  P. Petersen and F. Voigtlaender
  Proceedings of the AMS 148:1567-1581, 2020; doi: 10.1090/proc/14789

• Design and properties of wave packet smoothness spaces
  D. Bytchenkoff and F. Voigtlaender
  J. Math. Pures Appl. 133:185-262, 2020; doi: 10.1016/j.matpur.2019.05.006

• Optimal approximation of piecewise smooth functions using deep ReLU neural networks
  P. Petersen and F. Voigtlaender
  Neural Netw., 108:296-330, 2018; doi: 10.1016/j.neunet.2018.08.019

• Wavelet Coorbit Spaces viewed as Decomposition Spaces
  H. Führ and F. Voigtlaender
  J. Funct. Anal., 269(1):80-154, 2015; doi: 10.1016/j.jfa.2015.03.019

• Resolution of the Wavefront Set using general continuous Wavelet transforms
  J. Fell, H. Führ, and F. Voigtlaender
  J. Fourier. Anal. Appl., 22(5):997-1058, 2016; doi: 10.1007/s00041-015-9445-7

• Learning sparse representations on the sphere
  F. Sureau, F. Voigtlaender, M. Wust, J.-L. Starck, and G. Kutyniok
  Astron. Astrophys., 621:A73, 2019; doi: 10.1051/0004-6361/201834041

• From Frazier-Jawerth characterizations of Besov spaces to Wavelets and Decomposition spaces
  H.G. Feichtinger and F. Voigtlaender
  Contemp. Math., 693; doi: 10.1090/conm/693
  Part of the collection Functional Analysis, Harmonic Analysis, and Image Processing: A Collection of Papers in Honor of Björn Jawerth

• Identifying the root causes of wait states in large-scale parallel applications
  D. Böhme, M. Geimer, L. Arnold, F. Voigtlaender, and F. Wolf
  ACM Trans. Parallel Comput. 3, 2, Article 11 (July 2016); doi: 10.1145/2934661

Book Chapters

• On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel
  S. Dahlke, F. De Mari, E. De Vito, L. Sawatzki, G. Steidl, G. Teschke, and F. Voigtlaender
  Part of the book Landscapes of Time-Frequency Analysis, Pages 75-144; doi: 10.1007/978-3-030-05210-2_4

Preprints

• Upper and lower bounds for the Lipschitz constant of random neural networks
  P. Geuchen, T. Heindl, D. Stöger, and F. Voigtlaender

• Classification of anisotropic local Hardy spaces and inhomogeneous Triebel-Lizorkin spaces
  J. T. van Velthoven and F. Voigtlaender

• Lᵖ sampling numbers for the Fourier-analytic Barron space
  F. Voigtlaender

• Coorbit theory of warped time-frequency systems in ℝᵈ
  N. Holighaus and F. Voigtlaender

• Coorbit spaces and dual molecules: The quasi-Banach case
  J. T. van Velthoven and F. Voigtlaender

• Optimal learning of high-dimensional classification problems using deep neural networks
  P. Petersen and F. Voigtlaender

• Analysis vs. synthesis sparsity for α-shearlets
  F. Voigtlaender and A. Pein

• Embeddings of Decomposition Spaces into Sobolev and BV Spaces
  F. Voigtlaender

Thesis

• Embedding Theorems for Decomposition Spaces with applications to Wavelet Coorbit Spaces
  F. Voigtlaender, Ph.D. thesis

Conference proceedings

• Approximation in Lᵖ(μ) with deep ReLU neural networks
  F. Voigtlaender and P. Petersen
  Presented by F. Voigtlaender at SampTA 2019
  doi:10.1109/SampTA45681.2019.9030992

• The structure of spaces of neural network functions
  P. Petersen, M. Raslan, and F. Voigtlaender
  Presented by P. Petersen at the conference 11138 (Wavelets and Sparsity XVIII) at SPIE 2019
  doi:10.1117/12.2528313

• Unfavorable structural properties of the set of neural networks with fixed architecture
  P. Petersen, M. Raslan, and F. Voigtlaender
  Presented by M. Raslan at SampTA 2019
  doi:10.1109/SampTA45681.2019.9030975

• A quantitative Balian-Low theorem for subspaces
  A. Caragea, D.G. Lee, F. Philipp, and F. Voigtlaender
  Presented by A. Caragea at SampTA 2019
  doi:10.1109/SampTA45681.2019.9030951

• Time-Frequency Shift Invariance of Gabor Spaces
  A. Caragea, D.G. Lee, F. Philipp, and F. Voigtlaender
  Presented by F. Philipp at SampTA 2019
  doi:10.1109/SampTA45681.2019.9030919

• Understanding X-let sparsity via decomposition spaces
  F. Voigtlaender. Presented at SampTA 2017
  doi:10.1109/SAMPTA.2017.8024402

• Resolution of the wave front set using general wavelet transforms
  J. Fell, H. Führ and F. Voigtlaender.
  Presented by F. Voigtlaender at SampTA 2015
  doi:10.1109/SAMPTA.2015.7148907

Lecture series

• Lecture title: Approximation Properties of Neural Networks (lecture notes)
  F. Voigtlaender.
  Presented at the Workshop and Summer School on Applied Analysis 2023 in Chemnitz, Germany, 18-22 September, 2023.

• Lecture title: Sparsity Properties of Frames via Decomposition Spaces (lecture notes)
  F. Voigtlaender.
  Presented at the Summer School on Applied Harmonic Analysis: Three minicourses on Signal Analysis and Big Data in Genoa, Italy, 24-28 July, 2017.

Invited talks at international conferences and workshops

• Talk title: Optimal learning of high-dimensional classification problems using deep neural networks
  Talk presented at the Approximation theory workshop "Donau-Isar-Inn" (WDI² 2024)
  January 19, 2024
  Many thanks to Brigitte Forster and Thomas Sauer for inviting me!

• Talk title: Optimal learning of high-dimensional classification problems using deep neural networks
  Talk presented at the 11th Applied Inverse Problems Conference
  September 5, 2023
  Many thanks to Jakob Lemvig and Andreas Horst for inviting me!

• Talk title: Sampling numbers of the Fourier-type Barron spaces
  Online talk presented at the Codes and Expansions (CodEx) Seminar
  November 15, 2022
  Many thanks to Emily King and Dustin Mixon for inviting me!

• Talk title: The universal approximation theorem for complex-valued neural networks
  Online talk presented at the Focus Program on Data Science, Approximation Theory, and Harmonic Analysis at the Fields Institute for Research in Mathematical Sciences (University of Toronto)
  June 09, 2022
  

• Talk title: Minimax Rates for Learning Classifciation Functions using Neural Networks
  Online talk presented at the hybrid Follow-Up Workshop "Mathematics of Data Science" at the Hausdorff Research Institute for Mathematics (HIM)
  April 26, 2022
  

• Talk title: The universal approximation theorem for complex-valued neural networks
  Invited talk presented at the 2021 (online) meeting of the DMV (German Mathematical Society)
  September 29, 2021
  

• Talk title: Approximation theory of complex-valued neural networks
  Plenary talk presented at the Online International Conference on Computational Harmonic Analysis (Online-ICCHA2021)
  September 16, 2021
  

• Talk title: The Universal Approximation Theorem for complex-valued Neural Networks
  Talk presented at the Oberwolfach Workshop "Computation and Learning in High Dimensions"
  August 1-7, 2021, Oberwolfach, Germany

• Talk title: Coorbit dual molecules and convolution dominated operators
  Talk presented at the Online Workshop in Harmonic Analysis and its Applications
  December 3, 2020
  Many thanks to Reihaneh Raisi Tousi for inviting me!

• Talk title: Neural network performance for classification problems with boundaries of Barron class
  Talk presented at the One World Seminar Series on the Mathematics of Machine Learning
  November 25, 2020
  Many thanks to Philipp Petersen for inviting me!

• Talk title: Approximation in Lᵖ(μ) with deep ReLU neural networks
  Talk presented at the Workshop MAIA 2019 (Multivariate Approximation and Interpolation with Applications) at the Erwin Schrödinger Institute in Vienna
  August 30, 2019, Vienna, Austria
  Many thanks to Maria Charina, Philipp Grohs, and Karlheinz Gröchenig for inviting me!

• Talk title: Invertibility of frame operators on Besov-type decomposition spaces
  Talk presented at the 12th ISAAC Congress
  August 1, 2019, Aveiro, Portugal
  Many thanks to Daniel Abreu and Peter Balazs for inviting me!

• Talk title: Approximation spaces of deep neural networks
  Talk presented at the 90th annual meeting of the International Association of Applied Mathematics and Mechanics
  February 18, 2019, Vienna, Austria
  Many thanks to Philipp Petersen for inviting me!

• Talk title: Analyzing sparsity properties of frames using decomposition spaces
  Talk presented at the conference IWOTA 2018 (International Workshop on Operator Theory and its Applications)
  July 23, 2018, Shanghai, China
  Many thanks to Marcin Bownik for inviting me and to DAAD for providing the travel funds!

• Talk title: Approximation theoretic properties of deep ReLU neural networks
  Talk presented at the Workshop Donau-Isar-Inn Approximation Theory and Applications
  July 20, 2018, Munich, Germany
  Many thanks to Frank Filbir, Sara Krause-Solberg, and Nada Sissouno for inviting me!

• Talk title: Shearlets: Theory, applications and generalizations
  Talk presented at the conference Coherent States and their Applications: A Contemporary Panorama,
  November 15, 2016, CIRM, Marseille, France

Colloquium talks

• Talk title: Minimax rates for learning classification functions using neural networks
  Talk presented at the Mathematical Colloquium of the University of Ilmenau
  May 4, 2022, Ilmenau, Germany
  

• Talk title: Understanding sparsity properties of frames using decomposition spaces
  Talk presented at the Zurich colloquium in applied and computational mathematics
  March 6, 2019, Zürich, Switzerland
  Many thanks to Rima Alaifari for inviting me!

• Talk title: Approximation Theoretic Properties of Deep ReLU Neural Networks
  Talk presented at the Mathematical Colloquium at the Osnabrück University
  January 9, 2019, Osnabrück, Germany
  Many thanks to Stefan Kunis for inviting me!

• Talk title: Optimal approximation of piecewise smooth functions using deep ReLU neural networks
  Talk presented at the Zurich Colloquium in Applied and Computational Mathematics
  November 15, 2017, Zürich, Switzerland
  Many thanks to Rima Alaifari for inviting me!

Contributed talks at international conferences and workshops

• Talk title: Minimax rates for learning classification functions using neural networks
  Talk presented at the conference 8th International Conference on Computational Harmonic Analysis (ICCHA 2022),
  September 15, 2022, Ingolstadt, Germany

• Talk title: Dual molecules for (quasi-Banach) coorbit spaces
  Talk presented at the conference Strobl22 "Applied Harmonic Analysis and Friends",
  June 20, 2022, Strobl, Austria

• Talk title: Approximation in Lᵖ(μ) with deep ReLU neural networks
  Talk presented at the conference SampTA 2019,
  July 12, 2019, Bordeaux, France

• Talk title: A Guided Tour of Decomposition Spaces
  Talk presented at the conference Strobl18 Harmonic Analysis and Applications,
  June 7, 2018, Strobl, Austria

• Talk title: Approximation Properties of Deep ReLU Networks
  Talk presented at the Oberwolfach Workshop "Applied Harmonic Analysis and Data Processing"
  February 28, 2018, Oberwolfach, Germany

• Talk title: Structured Banach frame decompositions of decomposition spaces (slides)
  Talk presented at the conference NPFSA-2017 (New perspectives in the theory of function spaces and their applications),
  September 18, 2017, Będlewo, Poland

• Talk title: Understanding X-let sparsity via decomposition spaces
  Talk presented at the conference SampTA'17 (Sampling Theory and Applications),
  July 07, 2017, Tallinn, Estonia

• Talk title: Structured Banach frame decompositions of decomposition spaces (slides)
  Talk presented at the conference ATFA17 (Aspects of Time-Frequency Analysis),
  June 05, 2017, Politecnico di Torino, Italy

• Talk title: Embeddings of Decomposition Spaces
  Talk presented at FSDONA 2016,
  July 08, 2016, Charles University, Prague, Czech Republic

• Talk title: Embeddings of Decomposition Spaces
  Talk presented at the International Workshop on Mathematical Imaging and Emerging Modalities,
  June 30, 2016, Osnabrück, Germany

• Talk title: Embeddings of Decomposition Spaces
  Talk presented at Strobl16,
  June 06, 2016, Strobl, Austria

• Talk title: Resolution of the Wave Front Set using general Wavelet Transforms
  Talk presented at SampTA 2015,
  May 27, 2015, American University, Washington D.C., USA

• Talk title: Embeddings between decomposition spaces
  Talk presented at the conference Function Spaces and Harmonic Analysis,
  October 28, 2014, CIRM, Marseille, France

• Talk title: Coorbit spaces as decomposition spaces
  Talk presented at Strobl14,
  June 4, 2014, Strobl, Austria

Seminar talks

• Talk title: Optimal learning of high-dimensional classification problems using deep neural networks
  Talk presented at the Applied mathematics seminar of the University Utrecht
  February 15, 2024
  Many thanks to Sjoerd Dirksen for inviting me!

• Talk title: Minimax rates for learning classification functions using neural networks
  Talk presented at the Seminar (M15): Optimization and Data Analysis at TU Munich
  July 27, 2022
  Many thanks to Jan Vybiral for inviting me!

• Talk title: Sampling complexity on neural network approximation spaces
  Talk presented at the Seminar (M15): Optimization and Data Analysis at TU Munich
  June 17, 2021
  

• Talk title: Approximation theoretic and topological properties of neural networks
  Talk presented online at the seminar of the Chair for Mathematics of Information Processing
  September 3, 2020
  Many thanks to Holger Rauhut for inviting me!

• Talk title: Approximation theory of neural networks - from the concrete to the abstract
  Talk presented at the Deep Learning Seminar at University of Vienna
  October 2, 2019, Vienna, Austria
  Many thanks to Rafael Reisenhofer for inviting me!

• Talk title: Topological properties of the set of neural networks of fixed size
  Talk presented at the Deep Learning Seminar at University of Vienna
  February 26, 2019, Vienna, Austria
  Many thanks to Rafael Reisenhofer for inviting me!

• Talk title: Approximation theoretic properties of deep ReLU neural networks
  Talk presented at the Oberseminar "Dynamics" at TU Munich
  November 26, 2018, Munich, Germany
  Many thanks to Christian Kühn and Anne Pein for inviting me!

• Talk title: Understanding sparsity properties of frames using function spaces
  Talk presented at the Oberseminar "Optimization and Data Analysis" at TU Munich
  November 12, 2018, Munich, Germany
  Many thanks to Felix Krahmer for inviting me!

• Talk title: Approximation theoretic properties of deep ReLU neural networks
  Talk presented at the Seminar of the "Harmonic Analysis: Theory & Applications" group at DTU
  October 10, 2018, DTU, Copenhagen, Denmark
  Many thanks to Jakob Lemvig for inviting me!

• Talk title: Approximation theoretic properties of deep ReLU neural networks
  Talk presented at the Harmonic Analysis and Signal Processing Seminar at Courant Institute of Mathematical Sciences
  September 26, 2018, New York University, New York City, USA
  Many thanks to Sinan Güntürk for inviting me!

• Talk title: Understanding sparsity properties of frames using function spaces
  Talk presented at the applied mathematics seminar at Yale
  September 25, 2018, New Haven, CT, USA
  Many thanks to Gal Mishne and Stefan Steinerberger for inviting me!

• Talk title: Describing sparsity properties of frames using function spaces
  Talk presented at the Acoustic Research Institute
  February 21, 2018, Vienna, Austria
  Many thanks to N. Holighaus for inviting me!

• Talk title: Understanding sparsity properties of frames using decomposition spaces (slides)
  Talk presented at the graduate seminar "Advanced Topics in PDE and Harmonic Analysis"
  November 24, 2017, Bonn, Germany
  Many thanks to Tino Ullrich for inviting me!

• Talk title: Optimal approximation of piecewise smooth functions using deep ReLU neural networks (slides)
  Talk presented at the Research seminar "Mathematics of Computation",
  November 23, 2017, Bonn, Germany
  Many thanks to Tino Ullrich for inviting me!

• Talk title: Embeddings between decomposition spaces
  Talk presented at the Oberseminar Analysis, Geometrie und Stochastik,
  November 12, 2014, Friedrich-Schiller Universität Jena, Jena, Germany
  Many thanks to Daniel Lenz for inviting me!