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Publications (since 2023)

2026

• Constructive Approximation of High-Dimensional Functions with Small Efficient Dimension with Applications in Uncertainty Quantification, C. Rieger and H. Wendland, SIAM Journal on Numerical Analysis, 2026,  Link to preprint

2025

• Spectral stability and perturbation results for kernel differentiation matrices on the sphere, Numerische Mathematik, T. Hangelbroek, C. Rieger, G. Wright, 2025 (online first), Link to preprint
• Quarklet Characterizations for Bivariate Bessel-Potential Spaces on the Unit Square via Tensor Products,  Journal of Fourier Analysis and Applications, M. Hovemann (since Sept. 2024: Friedrich-Schiller-Universität Jena), 2025, Link to preprint
• Oscillations and differences in Besov-Morrey and Besov-type spaces, Analysis and Applications, M. Hovemann (since Sept. 2024: Friedrich-Schiller-Universität Jena), M. Weimar, 2025, Link to preprint

2024

• Adaptive Quarklet Tree Approximation,  Advances in Computational Mathematics, S. Dahlke, M. Hovemann, T. Raasch, D. Vogel, 2024 Link zum arXiv
• Kernel Multi-Grid on Manifolds, Journal of Complexity, Special Issue on Parabolic PDEs, T. Hangelbroek, C. Rieger, 2024, Link zum arXiv-Preprint
• On the Approximability and Curse of Dimensionality of Certain Classes of High-Dimensional Functions, SIAM Journal on Numerical Analysis, C. Rieger and H. Wendland, 2024.
• Some remarks on cone-adapted shearlets, GEM - International Journal on Geomathematics, S. Dahlke und G. Teschke
• Oscillations and differences in Triebel-Lizorkin-Morrey spaces,  Revista Matematica Complutense,  M. Hovemann and M. Weimar, 2024.
• Extending error bounds for radial basis function interpolation to measuring the error in higher order Sobolev norms, Mathematics of Computation, T. Hangelbroek and C. Rieger, 2024. Link zum arXiv-Preprint.
• Highly Localized RBF Lagrange Functions for Finite Difference Methods on Spheres, BIT Numerical Mathematics,  W. Erb, T. Hangelbroek, F. J. Narcowich, C. Rieger, J. D. Ward, 2024.  Link zum arXiv-Preprint.

2023

• Quarklet characterizations for Triebel–Lizorkin spaces, Journal of Approximation Theory, M. Hovemann, S. Dahlke, 2023
• B-Spline Quarklets and Biorthogonal Multiwavelets, International Journal of Wavelets, Multiresolution and Information Processing, M. Hovemann, A. Kopsch, T. Raasch, D. Vogel, 2023 (ArXiv)
• Anisotropic Besov regularity of parabolic PDEs, Pure and Applied Functional Analysis, S. Dahlke and C. Schneider 
• Nature 4.0: A networked sensor system for integrated biodiversity monitoring, Global Change Biology,
  D. Zeuss, L. Bald, J. Gottwald, M. Becker, H. Bellafkir, J. Bendix, P. Bengel, L. T. Beumer, R. Brandl, M. Brändle, S. Dahlke, N. Farwig, B. Freisleben, N. Friess, L. Heidrich, S. Heuer, J. Höchst, H. Holzmann, P. Lampe, M. Leberecht, K. Lindner, J. F. Masello, J. Mielke Möglich, M. Mühling, T. Müller, A. Noskov, L. Opgenoorth, C. Peter, P. Quillfeldt, S. Rösner, R. Royauté, C. Mestre-Runge, D. Schabo, D. Schneider, B. Seeger, E. Shayle, R. Steinmetz, P. Tafo, M. Vogelbacher, S. Wöllauer, S. Younis, J. Zobel, T. Nauss

Preprints

2025

• A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions, T. Hangelbroek, C. Rieger, G. B. Wright, 2025 (accepted for pulication in  SIAM Numerical Analysis)
• Efficiently parallelizable kernel-based multi-scale algorithm, F. Lot, C. Rieger, 2025 (accepted for publication in IMA Journal of Numerical Analysis)

2024

• On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data,
  M. Griebel, G. Li, C. Rieger, 2024
• Generalized local polynomial reproductions, T. Hangelbroek, C. Rieger, G. B. Wright, 2024 (accepted for pulication in  Foundations of Computational Mathematics)