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

Publications

Publications of Dr. Tino Ullrich:

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.
bib | .pdf 1 ]
[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.
bib | .pdf 1 ]
[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.
bib | .pdf 1 ]
[21] 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 ]
[22] D. Dung and T. Ullrich. Whitney type inequalities for local anisotropic polynomial approximation. Journ. Approx. Theory, 163(11):1590-1605, 2011.
bib | .pdf 1 ]
[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.
bib | .pdf 1 ]
[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.
bib | .pdf 1 ]
[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.
bib | .pdf 1 ]
[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.
bib | .pdf 1 ]

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.
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 ]