Navigation

Jump to main content
Professorship of Applied Analysis
Publications

Publications

Preprints:

[1] T. Jahn, T. Ullrich. On the optimal constants in the two-sided Stechkin inequalities. arXiv e-prints, 2020.
bib | arXiv ]
[2] N. Derevianko, T. Ullrich. Adaptive sampling recovery of functions with higher mixed regularity. arXiv e-prints, 2020.
bib | arXiv ]
[3] T. Kühn, W. Sickel, T. Ullrich. How anisotropic mixed smoothness affects the decay of singular numbers of Sobolev embeddings. arXiv e-prints, 2020.
bib | arXiv ]
[4] M. Schäfer, T. Ullrich, B. Vedel. Hyperbolic wavelet analysis of classical isotropic and anisotropic Besov-Sobolev spaces. arXiv e-prints, 2019.
bib | arXiv ]
[5] L. Kaemmerer, T. Ullrich, T. Volkmer. Worst case recovery guarantees for least squares approximation using random samples. arXiv e-prints, 2019.
bib | arXiv ]
[6] T. Ullrich. Local mean characterization of Besov-Triebel-Lizorkin type spaces with dominating mixed smoothness on rectangular domains. Preprint, pages 1-26, 2008.
bib | .pdf 1 ]

Books:

[1] D. Dung, V. N. Temlyakov, and T. Ullrich. Hyperbolic Cross Approximation. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer Basel, ISBN 978-3-319-92239-3, 2018.
bib | arXiv ]

Proceedings:

[1] G. Garrigós, A. Seeger, and T. Ullrich. Basis properties of the Haar system in limiting Besov spaces. Proceedings of the Conference Geometric Aspects of Harmonic Analysis, in honor of Fulvio Ricci, Springer INDAM series, to appear.
bib | arXiv ]

Journal Papers:

[1] N. Derevianko, T. Ullrich. A higher order Faber spline basis for sampling discretization of functions. J. Approx. Theory, to appear.
bib | arXiv ]
[2] S. Mayer and T. Ullrich. Entropy numbers of finite dimensional mixed-norm balls and function space embeddings with small mixed smoothness. Constr. Approx., to appear.
bib | arXiv ]
[3] C. Kacwin, J. Oettershagen, M. Ullrich, and T. Ullrich. Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces. Found. Comp. Math., to appear.
bib | .pdf 1 ]
[4] G. Garrigós, A. Seeger, T. Ullrich. The Haar System in Triebel-Lizorkin Spaces: Endpoint Results. Journ. Geom. Anal.,(special issue for Guido Weiss), to appear.
bib | arXiv ]
[5] G. Garrigós, A. Seeger, and T. Ullrich. The Haar system as a Schauder basis in spaces of Hardy-Sobolev type. J. Fourier. Anal. Appl., 24(5):1319–1339, 2018.
bib | arXiv ]
[6] S. Dirksen and T. Ullrich. Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness. J. Complexity, 48:69–102, 2018.
bib | arXiv ]
[7] H. Kempka, M. Schäfer, and T. Ullrich. General coorbit space theory for quasi-Banach spaces and inhomogeneous function spaces with variable smoothness and integrability. Journal of Fourier Analysis and Applications, 23(6):1348-1407, 2017.
bib ]
[8] A. Seeger and T. Ullrich. Haar projection numbers and failure of unconditional convergence in Sobolev spaces. Mathematische Zeitschrift, 285:91 - 119, 2017.
bib | arXiv ]
[9] G. Byrenheid, L. Kämmerer, T. Ullrich, and T. Volkmer. Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness. Num. Math., 136:993-1034, 2017.
bib | arXiv | .pdf 1 ]
[10] V. K. Nguyen, M. Ullrich, and T. Ullrich. Change of variable in spaces of mixed smoothnes and numerical integration of multivariate functions on the unit cube. Constructive Approximation, 46:69-108, 2017.
bib | arXiv | .pdf 1 ]
[11] A. Seeger and T. Ullrich. Lower bounds for Haar projections: deterministic examples. Constructive Approximation, 46:227–242, 2017.
bib | arXiv | .pdf 1 ]
[12] G. Byrenheid and T. Ullrich. Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood-Paley type characterizations. Anal. Math., 43(2):133-191, 2017.
bib | http ]
[13] C. Kacwin, J. Oettershagen and T. Ullrich. On the orthogonality of the Chebyshev-Frolov lattice and applications. Monatsh. Math., 184(3):425-441, 2017.
bib | http ]
[14] G. Garrigós, A. Seeger, and T. Ullrich. On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type. Analysis Mathematica, 43:267-278, 2017.
bib | arXiv ]
[15] G. Byrenheid, D. Dũng, W. Sickel, and T. Ullrich. Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in Hγ. J. Approx. Theory, 207:207-231, 2016.
bib | arXiv | .pdf 1 ]
[16] A. Hinrichs, L. Markhasin, J. Oettershagen, and T. Ullrich. Optimal quasi-Monte Carlo rules on higher order digital nets for the numerical integration of multivariate periodic functions. Num. Math, 134:163-196, 2016.
bib | arXiv ]
[17] M. Ullrich and T. Ullrich. The role of Frolov's cubature formula for functions with bounded mixed derivative. SIAM Journ. on Numerical Analysis, 54, No. 2:969-993, 2016.
bib | arXiv | .pdf 1 ]
[18] T. Kühn, S. Mayer, and T. Ullrich. Counting via entropy: new preasymptotics for the approximation numbers of Sobolev embeddings. SIAM Journ. on Numerical Analysis, 54(6):3625 - 3647, 2016.
bib | arXiv | .pdf 1 ]
[19] D. Dung and T. Ullrich. Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square. Math. Nachrichten, 288:743-762, 2015.
bib | arXiv | .pdf 1 ]
[20] T. Kühn, W. Sickel, and T. Ullrich. Approximation of mixed order Sobolev functions on the d-torus – asymptotics, preasymptotics and d-dependence. Constructive Approximation, 42:353-398, 2015.
bib | arXiv | .pdf 1 ]
[21] S. Mayer, T. Ullrich, and J. Vybiral. Entropy and sampling numbers of classes of ridge functions. Constructive Approximation, 42:231-264, 2015.
bib | DOI | arXiv | .pdf 1 ]
[22] T. Ullrich. Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square. J. Complexity, 30:72-94, 2014.
bib | .pdf 1 ]
[23] T. Kühn, W. Sickel, and T. Ullrich. Approximation numbers of Sobolev embeddings-sharp constants and tractability. J. Complexity, 30:95-116, 2014.
bib | .pdf 1 ]
[24] D. Dung and T. Ullrich. N-widths and ε-dimensions for high-dimensional approximations. Found. Comput. Math., 13:965-1003, 2013.
bib | .pdf 1 ]
[25] Y. Liang, Y. Sawano, T. Ullrich, D. Yang, and W. Yuan. A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces. Diss. Math., 489, 2013.
bib | .pdf 1 ]
[26] Y. Liang, Y. Sawano, T. Ullrich, D. Yang, and W. Yuan. New characterizations of Besov-Triebel-Lizorkin-Hausdorff spaces including coorbits and wavelets. J. Fourier Anal. Appl., 18(5):1067-1111, 2012.
bib | .pdf 1 ]
[27] T. Ullrich. Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits. Journ. Function Spaces and Applications, Article ID 163213, 2012.
bib | .pdf 1 ]
[28] D. Dung and T. Ullrich. Whitney type inequalities for local anisotropic polynomial approximation. Journ. Approx. Theory, 163(11):1590-1605, 2011.
bib | .pdf 1 ]
[29] W. Sickel and T. Ullrich. Spline interpolation on sparse grids. Applicable Analysis, 90(3-4):337-383, 2011.
bib | .pdf 1 ]
[30] T. Ullrich and H. Rauhut. Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type. J. Funct. Anal., 260(11):3299-3362, 2011.
bib | DOI | .pdf 1 ]
[31] S. Foucart, A. Pajor, H. Rauhut, and T. Ullrich. The Gelfand widths of lp-balls for 0 < p <=1. J. Complexity, 26:629-640, 2010.
bib | DOI | .pdf 1 ]
[32] F. Cobos, L. M. Fernandez-Cabrera, T. Kuehn, and T. Ullrich. On an extreme class of real interpolation spaces. Journal of Functional Analysis, 256:2321-2366, 2009.
bib | .pdf 1 ]
[33] F. Cobos, C. Richter, and T. Ullrich. Reiteration formulae for interpolation methods associated to polygons. Journal of Mathematical Analysis and Applications, 352:773-787, 2009.
bib | .pdf 1 ]
[34] W. Sickel and T. Ullrich. Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross. Journal of Approximation Theory, 161:748-786, 2009.
bib | .pdf 1 ]
[35] T. Ullrich. Smolyak's algorithm, sampling on sparse grids and Sobolev spaces of dominating mixed smoothness. East Journal on Approximations, 14(1):1-38, 2008.
bib | .pdf 1 ]
[36] W. Sickel and T. Ullrich. The Smolyak algorithm, sampling on sparse grids and function spaces of dominating mixed smoothness. East Journal on Approximations, 13(4):387-425, 2007.
bib | .pdf 1 ]

Conference contributions:

[1] S. Dirksen and T. Ullrich. Gelfand numbers, structured sparsity and Besov space embeddings with small mixed smoothness. 2017 International Conference on Sampling Theory and Applications (SampTA), pages 400-403, 2017.
bib ]

 

Thesis:

[1] T. Ullrich. Smolyak's algorithm, sparse grid approximation and periodic function spaces with dominating mixed smoothness. Friedrich-Schiller-Universität Jena, 2007. PhD thesis.
bib | .pdf 1 ]
[2] T. Ullrich. Über die periodische Interpolation auf schwach besetzten Gittern mittels de la Vallée Poussin-Kernen. Friedrich-Schiller-Universität Jena, 2004. Diploma thesis.
bib | .pdf 1 ]

Other Reports:

[1] T. Ullrich. Function spaces with dominating mixed smoothness, characterization by differences. Technical report, Jenaer Schriften zur Math. und Inform., Math/Inf/05/06, 2006.
bib | .pdf 1 ]
[2] T. Ullrich. Smolyak's algorithm, sparse grid approximation and periodic function spaces with dominating mixed smoothness. Technical report, Jenaer Schriften zur Math. und Inform., Math/Inf/15/06, 2006.
bib | .pdf 1 ]
[3] W. Sickel and T. Ullrich. The Smolyak algorithm, sampling on sparse grids and function spaces of dominating mixed smoothness. Technical report, Jenaer Schriften zur Math. und Inform., Math/Inf/14/06, 2006.
bib | .pdf 1 ]

Press Articles