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Veröffentlichungen "Voigtlaender, Felix"

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2023

Voigtlaender, Felix:
The universal approximation theorem for complex-valued neural networks.
In: Applied and computational harmonic analysis. 64 (2023). - S. 33-61.
ISSN 1063-5203 ; 1096-603x
10.1016/j.acha.2022.12.002
(Peer-Review-Journal)
Jahn, Thomas ; Ullrich, Tino ; Voigtlaender, Felix:
Sampling numbers of smoothness classes via ℓ1-minimization.
In: Journal of complexity. 79 (2023): 101786. - 35 S.
ISSN 0885-064x
10.1016/j.jco.2023.101786
(Peer-Review-Journal)
Abreu, Daniel Luìs ; Mouayn, Zouhair ; Voigtlaender, Felix:
A fractal uncertainty principle for Bergman spaces and analytic wavelets.
In: Journal of mathematical analysis and applications. 519 (2023) 1: 126699.
ISSN 0022-247x ; 1096-0813
10.1016/j.jmaa.2022.126699
(Peer-Review-Journal)
Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
A Balian–Low type theorem for Gabor Riesz sequences of arbitrary density.
In: Mathematische Zeitschrift. 303 (2023) 2: 48. - 23 S.
ISSN 1432-1823 ; 0025-5874
10.1007/s00209-022-03182-6
(Peer-Review-Journal)
Koppensteiner, Sarah ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
Anisotropic Triebel–Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I.
In: Monatshefte für Mathematik. 201 (2023). - S. 375-429.
ISSN 0026-9255 ; 1436-5081
10.1007/s00605-023-01827-0
(Peer-Review-Journal)
Koppensteiner, Sarah ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
Anisotropic Triebel–Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II.
In: Monatshefte für Mathematik. 201 (2023). - S. 431-464.
ISSN 0026-9255 ; 1436-5081
10.1007/s00605-023-01824-3
(Peer-Review-Journal)
Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
A Note on the Invertibility of the Gabor Frame Operator on Certain Modulation Spaces.
In: The journal of Fourier analysis and applications. 29 (2023): 3.
ISSN 1069-5869 ; 1531-5851
10.1007/s00041-022-09980-0
(Peer-Review-Journal)

2022

Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
Coorbit spaces and dual molecules : The quasi-Banach case.
2022. - 61 S.
arXiv:2203.07959
Caragea, Andrei ; Petersen, Philipp ; Voigtlaender, Felix:
Neural network approximation and estimation of classifiers with classification boundary in a Barron class.
2022. - 42 S.
arXiv:2011.09363
Gribonval, Rémi ; Kutyniok, Gitta ; Nielsen, Morten ; Voigtlaender, Felix:
Approximation Spaces of Deep Neural Networks.
In: Constructive approximation. 55 (2022). - S. 259-367.
ISSN 0176-4276 ; 1432-0940
10.1007/s00365-021-09543-4
(Peer-Review-Journal)
Caragea, Andrei ; Lee, Dae Gwan ; Maly, Johannes ; Pfander, Götz E. ; Voigtlaender, Felix:
Quantitative approximation results for complex-valued neural networks.
In: SIAM Journal on Mathematics of Data Science. 4 (2022) 2. - S. 553-580.
ISSN 2577-0187
0.1137/21M1429540
(Peer-Review-Journal)
Romero, José Luis ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
Invertibility of Frame Operators on Besov-Type Decomposition Spaces.
In: The journal of geometric analysis. 32 (2022) 5: 149.
ISSN 1559-002x ; 1050-6926
10.1007/s12220-022-00887-2
(Peer-Review-Journal)

2021

Grohs, Philipp ; Klotz, Andreas ; Voigtlaender, Felix:
Phase Transitions in Rate Distortion Theory and Deep Learning.
In: Foundations of computational mathematics. (16. November 2021). - 64 S.
ISSN 1615-3375 ; 1615-3383
10.1007/s10208-021-09546-4
(Peer-Review-Journal)
Koppensteiner, Sarah ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups.
2021. - 40 S.
arXiv:2104.14361
Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
A note on the invertibility of the Gabor frame operator on certain modulation spaces.
2021. - 17 S.
arXiv:2106.02365
Voigtlaender, Felix ; Petersen, Philipp:
Optimal learning of high-dimensional classification problems using deep neural networks.
2021. - 41 S.
arXiv:2112.12555
Grohs, Philipp ; Voigtlaender, Felix:
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces.
2021. - 42 S.
arXiv:2104.02746
Grohs, Philipp ; Voigtlaender, Felix:
Sobolev-type embeddings for neural network approximation spaces.
2021. - 14 S.
arXiv:2110.15304
Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
A quantitative subspace Balian-Low theorem.
In: Applied and computational harmonic analysis. 55 (2021). - S. 368-404.
ISSN 1063-5203 ; 1096-603x
10.1016/j.acha.2021.06.005
(Peer-Review-Journal)
Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
Topological properties of the set of functions generated by neural networks of fixed size.
In: Foundations of computational mathematics. 21 (2021). - S. 375-444.
ISSN 1615-3375 ; 1615-3383
10.1007/s10208-020-09461-0
(Peer-Review-Journal)
Romero, José Luis ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
On dual molecules and convolution-dominated operators.
In: Journal of functional analysis. 280 (2021) 10: 108963.
ISSN 0022-1236 ; 1096-0783
10.1016/j.jfa.2021.108963
(Peer-Review-Journal)
Holighaus, Nicki ; Voigtlaender, Felix:
Schur-type Banach modules of integral kernels acting on mixed-norm Lebesgue spaces.
In: Journal of functional analysis. 281 (2021) 9: 109197.
ISSN 0022-1236 ; 1096-0783
10.1016/j.jfa.2021.109197
(Peer-Review-Journal)
Almira, J. M. ; Lopez-de-Teruel, P. E. ; Romero-Lopez, D. J. ; Voigtlaender, Felix:
Negative results for approximation using single layer and multilayer feedforward neural networks.
In: Journal of mathematical analysis and applications. 494 (2021) 1: 124584.
ISSN 0022-247x ; 1096-0813
10.1016/j.jmaa.2020.124584
(Peer-Review-Journal)
Voigtlaender, Felix:
A General Version of Price’s Theorem.
In: Journal of theoretical probability. 34 (2021). - S. 1474-1485.
ISSN 0894-9840 ; 1572-9230
10.1007/s10959-020-01017-w
(Peer-Review-Journal)

2020

Voigtlaender, Felix:
The universal approximation theorem for complex-valued neural networks.
2020. - 29 S.
arXiv:2012.03351
Bytchenkoff, Dimitri ; Voigtlaender, Felix:
Design and properties of wave packet smoothness spaces.
In: Journal de mathématiques pures et appliquées. 133 (2020). - S. 185-262.
ISSN 0021-7824
10.1016/j.matpur.2019.05.006
(Peer-Review-Journal)
Petersen, Philipp ; Voigtlaender, Felix:
Equivalence of approximation by convolutional neural networks and fully-connected networks.
In: Proceedings of the American Mathematical Society. 148 (2020). - S. 1567-1581.
ISSN 0002-9939 ; 1088-6826
10.1090/proc/14789
(Peer-Review-Journal)

2019

Gribonval, Rémi ; Kutyniok, Gitta ; Nielsen, Morten ; Voigtlaender, Felix:
Approximation spaces of deep neural networks.
2019. - 64 S.
arXiv:1905.01208
Romero, José Luis ; Van Velthoven, Jordy Timo ; Voigtlaender, Felix:
Invertibility of frame operators on Besov-type decomposition spaces.
2019. - 54 S.
arXiv:1905.04934
Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
A quantitative subspace Balian-Low theorem.
2019. - 38 S.
10.48550/arXiv.1904.12250
Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
Time-frequency shift invariance of Gabor spaces with an S0-generator.
2019. - 15 S.
arXiv:1904.12345
Sureau, Florent ; Voigtlaender, Felix ; Wust, Malte ; Starck, Jean-Luc ; Kutyniok, Gitta:
Learning sparse representations on the sphere.
In: Astronomy & astrophysics. 621 (2019): A73. - 17 S.
ISSN 1432-0746
10.1051/0004-6361/201834041
(Peer-Review-Journal)
Dahlke, Stefan ; De Mari, Filippo ; De Vito, Ernesto ; Sawatzki, Lukas ; Steidl, Gabriele ; Teschke, Gerd ; Voigtlaender, Felix:
On the Atomic Decomposition of Coorbit Spaces with Non-Integrable Kernel.
In: Boggiatto, Paolo ; Cordero, Elena ; de Gosson, Maurice ; Feichtinger, Hans. G ; Nicola, Fabio ; Oliaro, Alessandro ; Tabacco, Anita (Hrsg.): Landscapes of Time-Frequency Analysis. - Basel : Birkhäuser, 2019. - S. 75-144. - (Applied and Numerical Harmonic Analysis)
ISBN 978-3-030-05209-6
10.1007/978-3-030-05210-2_4
(Begutachteter Beitrag / peer-reviewed paper)
Voigtlaender, Felix ; Petersen, Philipp:
Approximation in Lp(μ) with deep ReLU neural networks.
In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
ISBN 978-1-7281-3741-4
10.1109/SampTA45681.2019.9030992
(Begutachteter Beitrag / peer-reviewed paper)
Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
A quantitative Balian-Low theorem for subspaces.
In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
ISBN 978-1-7281-3741-4
10.1109/SampTA45681.2019.9030951
(Begutachteter Beitrag / peer-reviewed paper)
Caragea, Andrei ; Lee, Dae Gwan ; Philipp, Friedrich ; Voigtlaender, Felix:
Time-Frequency Shift Invariance of Gabor Spaces.
In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
ISBN 978-1-7281-3741-4
10.1109/SampTA45681.2019.9030919
(Begutachteter Beitrag / peer-reviewed paper)
Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
Unfavorable structural properties of the set of neural networks with fixed architecture.
In: Proceedings of International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, 2019. - Piscataway, NJ : IEEE, 2019
ISBN 978-1-7281-3741-4
10.1109/SampTA45681.2019.9030975
(Begutachteter Beitrag / peer-reviewed paper)
Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
The structure of spaces of neural network functions.
In: Proceedings of the conference SPIE 11138, Wavelets and Sparsity XVIII, 2019, San Diego, California, United States. - s.l. : SPIE, 2019
10.1117/12.2528313
(Begutachteter Beitrag / peer-reviewed paper)

2018

Petersen, Philipp ; Voigtlaender, Felix:
Optimal approximation of piecewise smooth functions using deep ReLU neural networks.
In: Neural networks. 108 (Dezember 2018). - S. 296-330.
ISSN 1879-2782 ; 0893-6080
10.1016/j.neunet.2018.08.019
(Peer-Review-Journal)
Petersen, Philipp ; Voigtlaender, Felix:
Equivalence of approximation by convolutional neural networks and fully-connected networks.
2018. - 13 S.
arXiv:1809.00973
Petersen, Philipp ; Raslan, Mones ; Voigtlaender, Felix:
Topological properties of the set of functions generated by neural networks of fixed size.
2018. - 51 S.
arXiv:1806.08459

2017

Voigtlaender, Felix:
Understanding X-let sparsity via decomposition spaces.
2017
Veranstaltung: 2017 International Conference on Sampling Theory and Applications (SampTA), 3-7 July 2017, Tallinn, Estonia.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung, Vortrag)
10.1109/SAMPTA.2017.8024402
Voigtlaender, Felix ; Pein, Anne:
Analysis vs. synthesis sparsity for α-shearlets.
2017. - 101 S.
arXiv:1702.03559
Feichtinger, Hans Georg ; Voigtlaender, Felix:
From Frazier-Jawerth characterizations of Besov spaces to Wavelets and Decomposition spaces.
In: Cwikel, Michael ; Milman, Mario (Hrsg.): Functional analysis, harmonic analysis, and image processing : a collection of papers in honor of Björn Jawerth. - Providence, Rhode Island : American Mathematical Society, 2017. - S. 185-216. - (Contemporary mathematics ; 693)
ISBN 978-1-4704-2836-5 ; 978-1-4704-4166-1
(Begutachteter Beitrag / peer-reviewed paper)

2016

Voigtlaender, Felix:
Embedding theorems for decomposition spaces with applications to wavelet coorbit spaces.
RWTH Aachen University
Aachen, 2016
urn:nbn:de:hbz:82-rwth-2015-075066
Voigtlaender, Felix:
Embeddings of Decomposition Spaces into Sobolev and BV Spaces.
2016. - 64 S.
arXiv:1601.02201
Böhme, David ; Geimer, Markus ; Arnold, Lukas ; Voigtlaender, Felix ; Wolf, Felix:
Identifying the Root Causes of Wait States in Large-Scale Parallel Applications.
In: ACM Transactions on Parallel Computing. 3 (2016) 2: 11. - 24 S.
ISSN 2329-4949 ; 2329-4957
10.1145/2934661
(Peer-Review-Journal)
Fell, Jonathan ; Führ, Hartmut ; Voigtlaender, Felix:
Resolution of the wavefront set using general continuous wavelet transforms.
In: The journal of Fourier analysis and applications. 22 (2016) 5. - S. 997-1058.
ISSN 1069-5869 ; 1531-5851
10.1007/s00041-015-9445-7
(Peer-Review-Journal)

2015

Fell, Jonathan ; Führ, Hartmut ; Voigtlaender, Felix:
Resolution of the wave front set using general wavelet transforms.
2015
Veranstaltung: 2015 International Conference on Sampling Theory and Applications (SampTA), 25-29 May 2015, Washington, DC, USA.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung, Vortrag)
10.1109/SAMPTA.2015.7148907
Führ, Hartmut ; Voigtlaender, Felix:
Wavelet coorbit spaces viewed as decomposition spaces.
In: Journal of functional analysis. 269 (2015) 1. - S. 80-154.
ISSN 0022-1236 ; 1096-0783
10.1016/j.jfa.2015.03.019
(Peer-Review-Journal)

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