Research Group of Dr. T. Ullrich
Institute for Numerical Simulation
maximize

Dr. Tino Ullrich

Dr. Tino Ullrich
Address: Hausdorff Center for Mathematics
Endenicher Allee 62
53115 Bonn
Germany
Office: Villa Maria 1.003
Phone: +49 228 73 62224
E-Mail: tino.ullrich.hcm.uni-bonn.de

News

Interim W3-Professor "Applied Analysis" at Osnabrück University

From April 2017 to September 2017 I am Interim Professor (W3) for Applied Analysis at Osnabrück University.

IBC workshop at FoCM 2017

Frances Kuo, Erich Novak and Tino Ullrich will be the organizers of the Information based Complexity workshop at the FoCM 2017, July 10-19th, Barcelona.

Mini-symposium on Preasymptotics at MCQMC 2016

For this year's MCQMC conference, held at Stanford university, Thomas Kühn (Leipzig) and Tino Ullrich have organized a mini-symposium on preasymptotics for multivariate approximation problems.

Plenary talk at SGA 2016

Tino Ullrich will be plenary speaker at the 4th Workshop on Sparse Grids and Applications in Miami (FL), October 4-7, 2016.

Advanced course on Hyperbolic Cross Approximation

Here you find the slides for the advanced course on Hyperbolic Cross Approximation, which Tino Ullrich gave together with Vladimir N. Temlyakov at the CRM Barcelona in May 2016.

IBC Young Researcher Award 2014

Tino Ullrich is the winner of the Information Based Complexity Young Researcher Award 2014.

Selected talks

[1] Sparse approximation with respect to the Faber-Schauder system. Invited talk at the Workshop "Function spaces and high-dimensional approximation" at the CRM Barcelona, 2016.
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[2] Preasymptotic error bounds for multivariate approximation problems. Dagstuhl Seminar 15391: Algorithms and Complexity for Continuous Problems, 2015.
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[3] Numerical Integration, Haar Projection Numbers and Failure of Unconditional Convergence. Plenary talk at the conference Harmonic Analysis and Approximations VI in Tsaghkadzor, Armenia, 2015.
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[4] Hyperbolic Cross Approximation. Plenary talk at the Information Based Complexity workshop in Bedlewo, Poland, 2015.
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Short CV

Teaching

Publications

Preprints:

[1] S. Dirksen and T. Ullrich. Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness. ArXiv e-prints, 2017. arXiv:1702.06781 [cs.IT].
bib | arXiv ]
[2] G. Garrigós, A. Seeger, and T. Ullrich. The Haar system as a Schauder basis in spaces of Hardy-Sobolev type. ArXiv e-prints, 2016. arXiv:1609.08225 [math.CA].
bib | arXiv ]
[3] T. Ullrich. Local mean characterization of Besov-Triebel-Lizorkin type spaces with dominating mixed smoothness on rectangular domains. Preprint, pages 1-26, 2008.
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Books:

[1] D. Dung, V. N. Temlyakov, and T. Ullrich. Hyperbolic Cross Approximation. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer, to appear.
bib | arXiv ]

Journal Papers:

[1] 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, to appear.
bib | arXiv ]
[2] 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., to appear.
bib | arXiv | .pdf 1 ]
[3] 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, to appear.
bib | arXiv | .pdf 1 ]
[4] A. Seeger and T. Ullrich. Lower bounds for Haar projections: deterministic examples. Constructive Approximation, to appear.
bib | arXiv | .pdf 1 ]
[5] G. Byrenheid and T. Ullrich. Optimal sampling recovery of mixed order Sobolev embeddings via discrete Littlewood-Paley type characterizations. Analysis Mathematica, to appear.
bib | arXiv ]
[6] C. Kacwin, J. Oettershagen, and T. Ullrich. On the orthogonality of the Chebyshev-Frolov lattice and applications. Monatshefte für Mathematik, to appear. arXiv:1606.00492 [math.NA].
bib | arXiv | .pdf 1 ]
[7] G. Garrigós, A. Seeger, and T. Ullrich. On uniform boundedness of dyadic averaging operators in spaces of Hardy-Sobolev type. Analysis Mathematica, to appear.
bib | arXiv ]
[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, 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 ]
[10] 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 ]
[11] 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 ]
[12] 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 ]
[13] 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 ]
[14] 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 ]
[15] 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 ]
[16] T. Ullrich. Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square. J. Complexity, 30:72-94, 2014.
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[17] T. Kühn, W. Sickel, and T. Ullrich. Approximation numbers of Sobolev embeddings-sharp constants and tractability. J. Complexity, 30:95-116, 2014.
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[18] D. Dung and T. Ullrich. N-widths and ε-dimensions for high-dimensional approximations. Found. Comput. Math., 13:965-1003, 2013.
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[19] 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.
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[20] 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.
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[21] T. Ullrich. Continuous characterizations of Besov-Lizorkin-Triebel spaces and new interpretations as coorbits. Journ. Function Spaces and Applications, Article ID 163213, 2012.
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[22] D. Dung and T. Ullrich. Whitney type inequalities for local anisotropic polynomial approximation. Journ. Approx. Theory, 163(11):1590-1605, 2011.
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[23] W. Sickel and T. Ullrich. Spline interpolation on sparse grids. Applicable Analysis, 90(3-4):337-383, 2011.
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[24] 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 ]
[25] 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 ]
[26] 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.
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[27] 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.
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[28] 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.
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[29] 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.
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[30] 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.
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Conference contributions:

[1] S. Dirksen and T. Ullrich. Gelfand numbers, structured sparsity and Besov space embeddings with small mixed smoothness. Proceedings of SampTA 2017, Tallinn (accepted).
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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.
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[2] T. Ullrich. Über die periodische Interpolation auf schwach besetzten Gittern mittels de la Vallée Poussin-Kernen. Friedrich-Schiller-Universität Jena, 2004. Diploma thesis.
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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.
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[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 ]