Publications
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D. Krieg, K. Pozharska, M. Ullrich, T. Ullrich. Sampling projections
in the uniform norm. arXiv e-prints, 2024.
arXiv |
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D. Krieg, K. Pozharska, M. Ullrich, T. Ullrich. Sampling recovery
in \(L_{2}\) and other norms. arXiv e-prints, 2023.
arXiv |
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N. Derevianko, T. Ullrich. Adaptive sampling recovery of
functions with higher mixed regularity. arXiv e-prints, 2020.
Bib |
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D. Dũng, V.N. Temlyakov, T. Ullrich. Hyperbolic Cross
Approximation. Advanced Courses in Mathematics. CRM Barcelona. Birkhäuser/Springer Basel, ISBN
978-3-319-92239-3, 2018.
Bib DOI arXiv |
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G. Garrigós, A. Seeger, T. Ullrich. Basis properties of
the Haar system in limiting Besov spaces. Chapter 11 in Geometric Aspects of Harmonic Analysis (in
honor of Fulvio Ricci), Springer INDAM series, ISBN 978-3-030-72058-2, 2021.
Bib DOI arXiv |
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F. Filbir, R. Hielscher, T. Jahn, T. Ullrich. Marcinkiewicz--Zygmund
inequalities for scattered and random data on the q-sphere. Appl. Comp. Harm. Anal. (ACHA) 71, 101651, 2024, ISSN 1063-5203.
Bib DOI arXiv |
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T. Jahn, T. Ullrich, F. Voigtlaender. Sampling numbers of smoothness
classes via \(\ell^{1}\)-minimization. J. Complexity, 79 (2023), Article 101786, ISSN
0885-064X.
Bib DOI arXiv |
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F. Bartel, L. Kämmerer, D. Potts, T. Ullrich. On the
reconstruction of functions from values at subsampled quadrature points. Math. Comp.
93
(2024), no. 346, 785–809.
Bib DOI arXiv |
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G. Byrenheid, S. Stasyuk, T. Ullrich. \(L_{p}\)-Sampling recovery
for non-compact subclasses of \(L_{\infty}\). Front. Appl. Math. Stat., 9:1216331, 2023.
Bib DOI arXiv |
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G. Garrigós, A. Seeger, T. Ullrich. A sufficient condition
for Haar multipliers in Triebel-Lizorkin spaces. To appear in a special volume to honor the
mathematics
of Guido Weiss, Birkhauser/Springer series, 2023.
arXiv |
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G. Garrigós, A. Seeger, T. Ullrich. Haar frame
characterizations of Besov–Sobolev spaces and optimal embeddings into their dyadic counterparts.
J Fourier Anal Appl 29, 39 (2023).
Bib DOI arXiv |
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L. Lippert, D. Potts, T. Ullrich. Fast hyperbolic wavelet regression
meets ANOVA. Numer. Math. 154, 155–207 (2023).
Bib DOI arXiv |
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F. Bartel, M. Schäfer, T. Ullrich. Constructive subsampling of
finite frames with applications in optimal function recovery. Applied and Computational Harmonic
Analysis, 65, 209-248, 2023.
Bib DOI arXiv |
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K. Pozharska, T. Ullrich. A note on sampling recovery of
multivariate functions in the uniform norm. SIAM J. Num. Anal., 60(3), 1363-1384, 2022.
Bib DOI arXiv |
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V. Temlyakov, T. Ullrich. Approximation of functions with small
mixed smoothness in the uniform norm. J. Approx. Theory, 277:105718, 2022.
Bib DOI arXiv |
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N. Nagel, M. Schäfer, T. Ullrich. A new upper bound for
sampling numbers. Found. Comput. Math., 22:445–468, 2022.
Bib DOI arXiv |
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T. Jahn, T. Ullrich. On the optimal constants in the two-sided
Stechkin inequalities. J. Approx. Theory, 269:105607, 2021.
Bib DOI arXiv |
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M. Moeller, T. Ullrich. \(L_{2}\)-norm sampling discretization and
recovery of functions from RKHS with finite trace. Sampl. Theory Signal Process. Data Anal.,
19:13,
2021.
Bib DOI arXiv |
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L. Kämmerer, T. Ullrich, T. Volkmer. Worst-case recovery
guarantees for least squares approximation using random samples. Constr. Approx.,
54:295–352,
2021.
Bib DOI arXiv |
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V. Temlyakov, T. Ullrich. Bounds on Kolmogorov widths and sampling
recovery for classes with small mixed smoothness. J. Complexity, 67:101575, 2021.
Bib DOI arXiv |
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M. Schäfer, T. Ullrich, B. Vedel. Hyperbolic wavelet analysis
of classical isotropic and anisotropic Besov–Sobolev spaces. J. Fourier Anal. Appl.,
27:51,
2021.
Bib DOI arXiv |
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T. Kühn, W. Sickel, T. Ullrich. How anisotropic mixed
smoothness affects the decay of singular numbers of Sobolev embeddings. J. Complexity,
63:101523,
2021.
Bib DOI arXiv |
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S. Mayer, T. Ullrich. Entropy numbers of finite dimensional
mixed-norm balls and function space embeddings with small mixed smoothness. Constr. Approx.,
53(2):249–279, 2021.
Bib DOI arXiv |
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C. Kacwin, J. Oettershagen, M. Ullrich, T. Ullrich. Numerical
performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces.
Found.
Comp. Math. 21:849–889, 2021.
Bib DOI arXiv PDF |
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G. Garrigós, A. Seeger, T. Ullrich. The Haar System in
Triebel–Lizorkin Spaces: Endpoint Results. J. Geom. Anal. 31:9045–9089, 2021.
Bib DOI arXiv |
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N. Derevianko, T. Ullrich. A higher order Faber spline basis for
sampling discretization of functions. J. Approx. Theory, 257:105449, 2020.
Bib DOI arXiv |
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G. Garrigós, A. Seeger, 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 DOI arXiv |
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S. Dirksen, T. Ullrich. Gelfand numbers related to structured
sparsity and Besov space embeddings with small mixed smoothness. J. Complexity,
48:69–102,
2018.
Bib DOI arXiv |
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H. Kempka, M. Schäfer, 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 DOI arXiv |
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A. Seeger, T. Ullrich. Haar projection numbers and failure of
unconditional convergence in Sobolev spaces. Mathematische Zeitschrift, 285:91–119,
2017.
Bib DOI arXiv |
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G. Byrenheid, L. Kämmerer, T. Ullrich, T. Volkmer. Tight
error bounds for rank-\(1\) lattice sampling in spaces of hybrid mixed smoothness. Num.
Math.,
136:993-1034, 2017.
Bib DOI arXiv PDF |
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V.K. Nguyen, M. Ullrich, T. Ullrich. Change of
variable in spaces of mixed smoothness and numerical integration of multivariate functions on the unit
cube.
Constructive Approximation, 46:69-108, 2017.
Bib DOI arXiv PDF |
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A. Seeger, T. Ullrich. Lower bounds for Haar projections:
deterministic examples. Constructive Approximation, 46:227–242, 2017.
Bib DOI arXiv PDF |
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G. Byrenheid, T. Ullrich. Optimal sampling recovery of mixed
order Sobolev embeddings via discrete Littlewood-Paley type characterizations. Anal. Math.,
43(2):133-191, 2017.
Bib DOI arXiv |
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C. Kacwin, J. Oettershagen, T. Ullrich. On the orthogonality of
the Chebyshev-Frolov lattice and applications. Monatsh. Math., 184(3):425-441, 2017.
Bib DOI arXiv |
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G. Garrigós, A. Seeger, T. Ullrich. On uniform boundedness
of dyadic averaging operators in spaces of Hardy-Sobolev type. Analysis Mathematica,
43:267-278,
2017.
Bib DOI arXiv |
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G. Byrenheid, D. Dũng, W. Sickel, T. Ullrich. Sampling on
energy-norm based sparse grids for the optimal recovery of Sobolev type functions in \(H^{\gamma}\).
J.
Approx. Theory, 207:207-231, 2016.
Bib DOI arXiv PDF |
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A. Hinrichs, L. Markhasin, J. Oettershagen, 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 DOI arXiv |
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M. Ullrich, 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 DOI arXiv PDF |
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T. Kühn, S. Mayer, 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 DOI arXiv PDF |
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D. Dũng, 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 DOI arXiv PDF |
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T. Kühn, W. Sickel, T. Ullrich. Approximation of mixed order
Sobolev functions on the \(d\)-torus – asymptotics, preasymptotics and d-dependence.
Constructive
Approximation, 42:353-398, 2015.
Bib DOI arXiv PDF |
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S. Mayer, T. Ullrich, J. Vybíral. Entropy and sampling
numbers of classes of ridge functions. Constructive Approximation, 42:231-264, 2015.
Bib DOI arXiv PDF |
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T. Ullrich. Optimal cubature in Besov spaces with dominating mixed
smoothness on the unit square. J. Complexity, 30:72-94, 2014.
Bib DOI PDF |
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T. Kühn, W. Sickel, T. Ullrich. Approximation numbers of
Sobolev embeddings – sharp constants and tractability. J. Complexity, 30:95-116, 2014.
Bib DOI PDF |
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D. Dũng, T. Ullrich. \(N\)-widths and
\(\varepsilon\)-dimensions for high-dimensional approximations. Found. Comput. Math.,
13:965-1003,
2013.
Bib DOI PDF |
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Y. Liang, Y. Sawano, T. Ullrich, D. Yang, W. Yuan. A new
framework for generalized Besov-type and Triebel–Lizorkin-type spaces. Diss. Math.,
489,
2013.
Bib DOI arXiv PDF |
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Y. Liang, Y. Sawano, T. Ullrich, D. Yang, W. Yuan. New
characterizations of Besov–Triebel–Lizorkin–Hausdorff spaces including coorbits and
wavelets. J. Fourier Anal. Appl., 18(5):1067-1111, 2012.
Bib DOI arXiv PDF |
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T. Ullrich. Continuous characterizations of
Besov–Lizorkin–Triebel spaces and new interpretations as coorbits. Journ. Function
Spaces
and Applications, Article ID 163213, 2012.
Bib DOI arXiv PDF |
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D. Dũng, T. Ullrich. Whitney type inequalities for local
anisotropic polynomial approximation. Journ. Approx. Theory, 163(11):1590-1605, 2011.
Bib DOI arXiv PDF |
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W. Sickel, T. Ullrich. Spline interpolation on sparse grids.
Applicable Analysis, 90(3-4):337-383, 2011.
Bib DOI PDF |
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T. Ullrich, 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 arXiv PDF |
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S. Foucart, A. Pajor, H. Rauhut, T. Ullrich. The Gelfand widths
of \(\ell_{p}\)-balls for \(0 < p \leq 1\). J. Complexity, 26:629-640, 2010.
Bib DOI arXiv PDF |
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F. Cobos, L.M. Fernandez-Cabrera, T. Kühn, T. Ullrich. On an
extreme class of real interpolation spaces. Journal of Functional Analysis, 256:2321-2366,
2009.
Bib DOI PDF |
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F. Cobos, C. Richter, T. Ullrich. Reiteration formulae for
interpolation methods associated to polygons. Journal of Mathematical Analysis and
Applications,
352:773-787, 2009.
Bib DOI PDF |
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W. Sickel, 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 |
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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 |
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W. Sickel, 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 |
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F. Bartel, K. Lüttgen, N. Nagel, T. Ullrich. Efficient recovery of
non-periodic multivariate functions from few scattered samples. 2023 International Conference on
Sampling Theory and Applications (SampTA), New Haven, CT, USA, 2023, pp. 1-6.
Bib DOI arXiv |
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S. Dirksen, 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 DOI |
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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 |
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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 |
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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 |
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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 |
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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 |
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W. Sickel, 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 |