Tino Ullrich's Publications
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List of Publications
D. Krieg, K. Pozharska, M. Ullrich, T. Ullrich
Sampling projections in the uniform norm
arXiv e-prints, 2024
D. Krieg, K. Pozharska, M. Ullrich, T. Ullrich
Sampling recovery in \(L_{2}\) and other norms
arXiv e-prints, 2023
N. Derevianko, T. Ullrich
Adaptive sampling recovery of functions with higher mixed regularity
arXiv e-prints, 2020
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
T. Jahn, T. Ullrich, F. Voigtlaender
Sampling numbers of smoothness classes via \(\ell^{1}\)-minimization
J. Complexity, 79 (2023), Article 101786, ISSN 0885-064X
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
G. Byrenheid, S. Stasyuk, T. Ullrich
\(L_{p}\)-Sampling recovery for non-compact subclasses of \(L_{\infty}\)
Front. Appl. Math. Stat., 9:1216331, 2023
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
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)
L. Lippert, D. Potts, T. Ullrich
Fast hyperbolic wavelet regression meets ANOVA
Numer. Math. 154, 155–207 (2023)
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
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
V. Temlyakov, T. Ullrich
Approximation of functions with small mixed smoothness in the uniform norm
J. Approx. Theory, 277:105718, 2022
N. Nagel, M. Schäfer, T. Ullrich
A new upper bound for sampling numbers
Found. Comput. Math., 22:445–468, 2022
T. Jahn, T. Ullrich
On the optimal constants in the two-sided Stechkin inequalities
J. Approx. Theory, 269:105607, 2021
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
L. Kämmerer, T. Ullrich, T. Volkmer
Worst-case recovery guarantees for least squares approximation using random samples
Constr. Approx., 54:295–352, 2021
V. Temlyakov, T. Ullrich
Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness
J. Complexity, 67:101575, 2021
M. Schäfer, T. Ullrich, B. Vedel
Hyperbolic wavelet analysis of classical isotropic and anisotropic Besov–Sobolev spaces
J. Fourier Anal. Appl., 27:51, 2021
T. Kühn, W. Sickel, T. Ullrich
How anisotropic mixed smoothness affects the decay of singular numbers of Sobolev embeddings
J. Complexity, 63:101523, 2021
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
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
G. Garrigós, A. Seeger, T. Ullrich
The Haar System in Triebel–Lizorkin Spaces: Endpoint Results
J. Geom. Anal. 31:9045–9089, 2021
N. Derevianko, T. Ullrich
A higher order Faber spline basis for sampling discretization of functions
J. Approx. Theory, 257:105449, 2020
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
S. Dirksen, T. Ullrich
Gelfand numbers related to structured sparsity and Besov space embeddings with small mixed smoothness
J. Complexity, 48:69–102, 2018
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
A. Seeger, T. Ullrich
Haar projection numbers and failure of unconditional convergence in Sobolev spaces
Mathematische Zeitschrift, 285:91–119, 2017
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
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
A. Seeger, T. Ullrich
Lower bounds for Haar projections: deterministic examples
Constructive Approximation, 46:227–242, 2017
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
C. Kacwin, J. Oettershagen, T. Ullrich
On the orthogonality of the Chebyshev-Frolov lattice and applications
Monatsh. Math., 184(3):425-441, 2017
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
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
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
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
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
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
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
S. Mayer, T. Ullrich, J. Vybíral
Entropy and sampling numbers of classes of ridge functions
Constructive Approximation, 42:231-264, 2015
T. Ullrich
Optimal cubature in Besov spaces with dominating mixed smoothness on the unit square
J. Complexity, 30:72-94, 2014
T. Kühn, W. Sickel, T. Ullrich
Approximation numbers of Sobolev embeddings – sharp constants and tractability
J. Complexity, 30:95-116, 2014
D. Dũng, T. Ullrich
\(N\)-widths and \(\varepsilon\)-dimensions for high-dimensional approximations
Found. Comput. Math., 13:965-1003, 2013
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
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
T. Ullrich
Continuous characterizations of Besov–Lizorkin–Triebel spaces and new interpretations as coorbits
Journ. Function Spaces and Applications, Article ID 163213, 2012
D. Dũng, T. Ullrich
Whitney type inequalities for local anisotropic polynomial approximation
Journ. Approx. Theory, 163(11):1590-1605, 2011
W. Sickel, T. Ullrich
Spline interpolation on sparse grids
Applicable Analysis, 90(3-4):337-383, 2011
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
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
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
F. Cobos, C. Richter, T. Ullrich
Reiteration formulae for interpolation methods associated to polygons
Journal of Mathematical Analysis and Applications, 352:773-787, 2009
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
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
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
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
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
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
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
T. Ullrich
Smolyak's algorithm, sparse grid approximation and periodic function spaces with dominating mixed smoothness
Friedrich-Schiller-Universität Jena, 2007. PhD thesis
T. Ullrich
Über die periodische Interpolation auf schwach besetzten Gittern mittels de la Vallée Poussin-Kernen
Friedrich-Schiller-Universität Jena, 2004. Diploma thesis
T. Ullrich
Local mean characterization of Besov–Triebel–Lizorkin type spaces with dominating mixed smoothness on rectangular domains
Preprint, pages 1-26, 2008
T. Ullrich
Function spaces with dominating mixed smoothness, characterization by differences
Technical report, Jenaer Schriften zur Math. und Inform., Math/Inf/05/06, 2006
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
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
