| Publication | Date of Publication | Type |
|---|
| Stable Gabor phase retrieval in Gaussian shift-invariant spaces via biorthogonality | 2024-03-05 | Paper |
| Sampling Complexity of Deep Approximation Spaces | 2023-12-20 | Paper |
| Non-Uniqueness Theory in Sampled STFT Phase Retrieval | 2023-10-17 | Paper |
| Phase retrieval in Fock space and perturbation of Liouville sets | 2023-08-01 | Paper |
| Lower bounds for artificial neural network approximations: a proof that shallow neural networks fail to overcome the curse of dimensionality | 2023-06-07 | Paper |
| Sobolev-type embeddings for neural network approximation spaces | 2023-04-27 | Paper |
| A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations | 2023-04-26 | Paper |
| The Modern Mathematics of Deep Learning | 2023-03-06 | Paper |
| Phase transitions in rate distortion theory and deep learning | 2023-02-16 | Paper |
| Space-time error estimates for deep neural network approximations for differential equations | 2023-02-03 | Paper |
| Injectivity of Gabor phase retrieval from lattice measurements | 2022-12-08 | Paper |
| From completeness of discrete translates to phaseless sampling of the short-time Fourier transform | 2022-11-10 | Paper |
| The modern mathematics of deep learning | 2022-08-15 | Paper |
| Uniform error estimates for artificial neural network approximations for heat equations | 2022-07-26 | Paper |
| Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions | 2022-07-26 | Paper |
| Multi-window STFT phase retrieval: lattice uniqueness | 2022-07-21 | Paper |
| Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms | 2022-07-08 | Paper |
| Approximations with deep neural networks in Sobolev time-space | 2022-05-16 | Paper |
| Stable Gabor phase retrieval for multivariate functions | 2022-04-19 | Paper |
| On foundational discretization barriers in STFT phase retrieval | 2022-04-11 | Paper |
| DNN expression rate analysis of high-dimensional PDEs: application to option pricing | 2022-03-21 | Paper |
| Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations | 2022-03-01 | Paper |
| RICAM, the Johann Radon Institute for Computational and Applied Mathematics | 2022-02-17 | Paper |
| Optimal Approximation with Sparsely Connected Deep Neural Networks | 2022-02-03 | Paper |
| Integral representations of shallow neural network with Rectified Power Unit activation function | 2021-12-20 | Paper |
| Sobolev-type embeddings for neural network approximation spaces | 2021-10-28 | Paper |
| Solving the Kolmogorov PDE by means of deep learning | 2021-09-01 | Paper |
| $L^2$-stability analysis for Gabor phase retrieval | 2021-08-13 | Paper |
| Deep Neural Network Approximation Theory | 2021-07-22 | Paper |
| Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces | 2021-04-06 | Paper |
| Gabor phase retrieval is severely ill-posed | 2021-03-26 | Paper |
| Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations | 2021-03-09 | Paper |
| Phase Transitions in Rate Distortion Theory and Deep Learning | 2020-08-03 | Paper |
| Phase Retrieval: Uniqueness and Stability | 2020-06-03 | Paper |
| Anisotropic multiscale systems on bounded domains | 2020-05-11 | Paper |
| Analysis of edge and corner points using parabolic dictionaries | 2020-02-28 | Paper |
| Space-time error estimates for deep neural network approximations for differential equations | 2019-08-10 | Paper |
| Stable phase retrieval in infinite dimensions | 2019-08-09 | Paper |
| Tensor-Product Discretization for the Spatially Inhomogeneous and Transient Boltzmann Equation in Two Dimensions | 2019-07-03 | Paper |
| Stable Gabor Phase Retrieval and Spectral Clustering | 2019-06-07 | Paper |
| Projection-Based Finite Elements for Nonlinear Function Spaces | 2019-02-20 | Paper |
| On the approximation of functions with line singularities by ridgelets | 2018-10-26 | Paper |
| Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds | 2018-09-26 | Paper |
| Energy Propagation in Deep Convolutional Neural Networks | 2018-09-19 | Paper |
| A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations | 2018-09-07 | Paper |
| Total variation regularization on Riemannian manifolds by iteratively reweighted minimization | 2018-03-08 | Paper |
| Reconstructing real-valued functions from unsigned coefficients with respect to wavelet and other frames | 2018-01-25 | Paper |
| Topology Reduction in Deep Convolutional Feature Extraction Networks | 2017-07-10 | Paper |
| Phase Retrieval In The General Setting Of Continuous Frames For Banach Spaces | 2017-06-09 | Paper |
| Scattered manifold-valued data approximation | 2017-04-13 | Paper |
| Cartoon approximation with \(\alpha\)-curvelets | 2017-01-10 | Paper |
| Optimal adaptive ridgelet schemes for linear advection equations | 2016-10-12 | Paper |
| A shearlet-based fast thresholded Landweber algorithm for deconvolution | 2016-09-28 | Paper |
| \(\alpha\)-Molecules | 2016-05-19 | Paper |
| \(\varepsilon\)-subgradient algorithms for locally Lipschitz functions on Riemannian manifolds | 2016-04-22 | Paper |
| From Group Representations to Signal Analysis | 2016-01-26 | Paper |
| Optimally Sparse Data Representations | 2016-01-26 | Paper |
| Optimal a priori discretization error bounds for geodesic finite elements | 2015-12-04 | Paper |
| Hyperbolic cross approximation for the spatially homogeneous Boltzmann equation | 2015-11-06 | Paper |
| Parabolic Molecules: Curvelets, Shearlets, and Beyond | 2015-10-09 | Paper |
| Ridgelet Methods for Linear Transport Equations | 2015-09-15 | Paper |
| Wolfowitz’s theorem and consensus algorithms in Hadamard spaces | 2015-09-08 | Paper |
| Intrinsic localization of anisotropic frames. II: \(\alpha\)-molecules | 2015-03-02 | Paper |
| Parabolic molecules | 2014-09-04 | Paper |
| Intrinsic localization of anisotropic frames | 2014-07-16 | Paper |
| Geometric multiscale decompositions of dynamic low-rank matrices | 2014-04-04 | Paper |
| Quasi-interpolation in Riemannian manifolds | 2013-07-24 | Paper |
| Refinable functions for dilation families | 2013-05-06 | Paper |
| Bandlimited shearlet-type frames with nice duals | 2013-02-21 | Paper |
| Definability and stability of multiscale decompositions for manifold-valued data | 2012-12-28 | Paper |
| Ruled Laguerre minimal surfaces | 2012-10-22 | Paper |
| Interpolating Composite Systems | 2012-09-14 | Paper |
| Shearlets and Microlocal Analysis | 2012-09-06 | Paper |
| Tree approximation with anisotropic decompositions | 2012-06-13 | Paper |
| Ridgelet-type frame decompositions for Sobolev spaces related to linear transport | 2012-04-26 | Paper |
| Continuous shearlet frames and resolution of the wavefront set | 2011-12-14 | Paper |
| Continuous shearlet tight frames | 2011-10-11 | Paper |
| Edge offset meshes in Laguerre geometry | 2011-06-07 | Paper |
| A General Proximity Analysis of Nonlinear Subdivision Schemes | 2011-03-25 | Paper |
| Stability of manifold-valued subdivision schemes and multiscale transformations | 2010-11-22 | Paper |
| Approximation order from stability for nonlinear subdivision schemes | 2010-06-17 | Paper |
| Approximation order of interpolatory nonlinear subdivision schemes | 2010-01-15 | Paper |
| Laguerre minimal surfaces, isotropic geometry and linear elasticity | 2010-01-04 | Paper |
| Interpolatory wavelets for manifold-valued data | 2009-10-20 | Paper |
| Smoothness equivalence properties of univariate subdivision schemes and their projection analogues | 2009-09-14 | Paper |
| Smoothness Analysis of Subdivision Schemes on Regular Grids by Proximity | 2009-08-20 | Paper |
| Smoothness of interpolatory multivariate subdivision in Lie groups | 2009-08-03 | Paper |
| https://portal.mardi4nfdi.de/entity/Q3509289 | 2008-07-01 | Paper |
| Smoothness Properties of Lie Group Subdivision Schemes | 2008-06-10 | Paper |
