Publications:

The published versions of the papers may slightly differ from the downloadable files below.



Papers:

52. with A. Hinrichs and J. Prochno
Gelfand numbers of embeddings of Schatten classes
submitted, available at arXiv
51. with A. Hinrichs, D. Krieg, and E. Novak
Lower bounds for the error of quadrature formulas for Hilbert spaces
submitted, available at arXiv
50. A variant of Schur's product theorem and its applications
Adv. Math. 368 (2020), 107140, available at arXiv
49. with Anna Doležalová
On the volume of unit balls of finite-dimensional Lorentz spaces
J. Appr. Theory 255 (2020), 105407, available at arXiv
48. with Mario Ullrich
Deterministic constructions of high-dimensional sets with small dispersion
submitted, available at arXiv
47. with Aicke Hinrichs, Joscha Prochno, and Mario Ullrich
The minimal k-dispersion of point sets in high-dimensions
J. Compl. 51 (2019), 68-78, available at arXiv
46. with M. Fornasier and I. Daubechies
Robust and resource efficient identification of shallow neural networks by fewest samples
to appear in Information and Inference: a Journal of the IMA, available at arXiv
45. with M. Kossaczka
Entropy numbers of finite-dimensional embeddings
Expositiones Mathematicae 38(3) (2020), 319-336, available at arXiv .pdf
44. with H. Tyagi
Learning non-smooth sparse additive models from point queries in high dimensions
Constr. Appr. 50(3) (2019), 403-455, available at arXiv .pdf
43. with M. Ullrich
An upper bound on the minimal dispersion
J. Compl. 45 (2018), 120-126, available at arXiv .pdf
42. with L. M. Ghiringhelli, E. Ahmetchik, R. Ouyang, S. V. Levchenko, C. Draxl, and M. Scheffler
Learning physical descriptors for materials science by compressed sensing
New Journal of Physics, 19 (2017), 023017, available at arXiv.pdf
41. with A. Hinrichs and J. Prochno
Entropy numbers of embeddings of Schatten classes
J. Funct. Anal. 273 (10) (2017), 3241-3261, available at arXiv.pdf
40. with H. F. Goncalves and H. Kempka
Franke-Jawerth embeddings for Besov and Triebel-Lizorkin spaces with variable exponents
Ann. Acad. Sci. Fenn. Math. 43(1) (2018), 187-209, available at arXiv .pdf
39. with T. Conrad, M. Genzel, N. Cvetkovic, N. Wulkow, A. Leichtle, G. Kutyniok, and Ch. Schuette
Sparse Proteomics Analysis - A compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data
BMC Bioinformatics 18:160 (2017), available at arXiv
38. with A. Hinrichs and A. Kolleck
Carl's inequality for quasi-Banach spaces
J. Funct. Anal. 271 (8) (2016), 2293-2307, available at arXiv.pdf
37. with A. Kolleck
Non-asymptotic Analysis of l1-norm Support Vector Machines
IEEE Trans. Inf. Theory 63, no. 9 (2017), 5461-5476, available at arXiv
36. with H. Kempka
Volumes of unit balls of mixed sequence spaces
Math. Nachr. 290, no. 8-9 (2017), 1317-1327, available at arXiv .ps and .pdf
35. with A. Kolleck
On some aspects of approximation of ridge functions
J. Appr. Theory 194 (2015), 35-61 .pdf
34. with L. M. Ghiringhelli, S. V. Levchenko, C. Draxl, and M. Scheffler
Big data of materials science - Critical role of the descriptor
Phys. Rev. Lett. 114, 105503 (2015), available at arXiv .pdf
33. with H. Boche, R. Calderbank, and G. Kutyniok
A Survey of Compressed Sensing
First chapter in Compressed Sensing and its Applications, Birkhäuser, Springer, 2015 .pdf
32. with S. Mayer, T. Ullrich
Entropy and sampling numbers of classes of ridge functions
Constructive Approximation 42 (2) (2015), 231-264, available at arXiv .pdf
31. Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions
J. Compl. 30 (2) (2014), 48-55, available at arXiv .ps and .pdf
30. with W. Sickel and L. Skrzypczak
Complex Interpolation of Weighted Besov- and Lizorkin-Triebel Spaces
Acta Math. Sin. (Engl. Ser.) 30 (8) (2014), 1297-1323, available at arXiv .ps and .pdf
29. with W. Sickel and L. Skrzypczak
The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences
Banach Center Publ. 102 (2014), 197-214, available at arXiv .ps and .pdf
28. with H. Kempka
Lorentz spaces with variable exponents
Math. Nachr. 287, no. 8-9 (2014), 938-954, available at arXiv .ps and .pdf
27. with C. Schneider
Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces
J. Funct. Anal. 264 (5) (2013),1197-1237, available at arXiv .ps and .pdf
26. with C. Schneider
Homogeneity property of Besov and Triebel-Lizorkin spaces
J. Funct. Spaces Appl. Volume 2012, Article ID 281085, 17 pages, available at arXiv .ps and .pdf
25. with M. Fornasier and J. Haskovec
Particle systems and kinetic equations modeling interacting agents in high dimension
SIAM: Multiscale Modeling and Simulation 9(4)(2011), 1727-1764, available at arXiv .ps and .pdf
24. with H. Kempka
Spaces of variable smoothness and integrability: Characterizations by local means and ball means of differences
J. Fourier Anal. Appl. 18 (4) (2012), 852-891, available at arXiv .ps and .pdf
23. with H. Kempka
A note on the spaces of variable integrability and summability of Almeida and H\"ast\"o
Proc. Amer. Math. Soc. 141 (9) (2013), 3207-3212, available at arXiv .ps and .pdf
22. Average best m-term approximation
Constructive Approximation 36 (1) (2012), 83-115, available at arXiv .ps and .pdf
21. with M. Fornasier and K. Schnass
Learning functions of few arbitrary linear parameters in high dimensions
Found. Comput. Math. 12 (2) (2012), 229-262, available at arXiv .ps and .pdf
20. with W. Sickel and L. Skrzypczak
On the interplay of regularity and decay in case of radial functions I. Inhomogeneous spaces
Commun. Contemp. Math. 14 (1) (2012), 1250005 (60 Pages), available at arXiv .ps and .pdf
19. A variant of the Johnson-Lindenstrauss lemma for circulant matrices
J. Funct. Anal. 260(4) (2011), 1096-1105, available at arXiv .ps and .pdf
18. with A. Hinrichs
Johnson-Lindenstrauss lemma for circulant matrices
Random Struct. Algor. 39(3) (2011), 391-398, available at arXiv .ps and .pdf
17. with A. Hinrichs
On positive positive-definite functions and Bochner's Theorem
J. Compl. 27 (2011), 264-272 .ps and .pdf
16. with S. Hencl, J. Maly and L. Pick
Weak estimates cannot be obtained by extrapolation
Expo. Math., 28 (2010), 375–377 .ps and .pdf
15. with C. Schneider
On dilation operators in Triebel-Lizorkin spaces
Funct. Approx., 41(2) (2009), 139-162. .ps and .pdf
14. Sobolev and Jawerth embeddings for spaces with variable smoothness and integrability
Ann. Acad. Sci. Fenn. Math. 34:2 (2009), 529-544. .ps and .pdf
13. On sharp embeddings of Besov and Triebel-Lizorkin spaces in the subcritical case
Proc. Amer. Math. Soc. 138 (2010), 141-146. .ps and .pdf
12. with M. Hansen
The Jawerth-Franke embedding of spaces with dominating mixed smoothness
Georg. Math. J. 16 (2009), No. 4, 667--682 .ps and .pdf
11. with L. Skrzypczak
Corrigenda to the paper: "On approximation numbers of Sobolev embeddings of weighted function spaces"
J. Approx. Theory 156 (2009), 116-119. .ps and .pdf
10. with A. Hinrichs and E. Novak
Linear information versus function evaluations for L_2-approximation
J. Approx. Theory 153 (2008), 97-107. .ps and .pdf
9. Widths of embeddings in function spaces
J. Compl. 24 (2008), 545-570. .ps and .pdf
8. A new proof of Jawerth-Franke embedding
Rev. Mat. Complut. 21 (2008), 75-82. .ps and .pdf
7. Dilation operators and sampling numbers
J. of Function Spaces and Appl. 6 (2008), 17-46. .ps and .pdf
6. Sampling numbers and function spaces
J. Compl. 23 (2007), 773-792. .ps and .pdf
5. with W. Sickel
Traces of function spaces with dominating mixed derivative in R3
Czechoslovak Math. J., Vol. 57, No. 4 (2007), 1239-1273. .ps and .pdf
4. Optimal Sobolev embeddings on Rn
Publ. Mat. 51 (2007), 17-44. .ps and .pdf
3. A diagonal embedding theorem for function spaces with dominating mixed smoothness
Funct. et Appr. 33 (2005), 101-120. .ps and .pdf
2. A remark on better-lambda inequality
Math. Ineq. Appl. 10 (2007), 335-341. .ps and .pdf
1. Function spaces with dominating mixed smoothness
Diss. Math. 436 (2006), 1-73. .ps and .pdf

Theses:

Functions and sequences in analysis and applications, Habilitation thesis, Survey, Prague, 2015.

Decomposition methods and their applications in the theory of function spaces, Habilitation thesis in .pdf, Jena, 2011.

Fine properties of Sobolev embeddings, Abstract of the doctoral thesis in .ps and .pdf, Prague, 2008.

Function spaces with dominating mixed smoothness, Dr. Thesis, Jena, 2005. .ps and .pdf

Optimality of Function Spaces for Boundedness of Integral Operators and Sobolev Embeddings, Master Thesis, Prague, 2002. .ps and .pdf



Conference proceedings, preprints and others... :

4. with M. Fornasier and K. Schnass, Learning functions of few arbitrary linear parameters in high dimensions, .ps and .pdf, Proceedings of SampTA 2011.

3. Generating random signals and sparse and compressible vectors, .pdf, Proceedings of SampTA 2011.

2. with K. Schnass, Compressed Learning of High-Dimensional Sparse Functions .pdf, Proceedings of ICASSP 2011.

1. Characterisations of function spaces with dominating mixed smoothness properties, Jenaer Schriften zur Mathematik und Informatik, Math/Inf/15/03, 2003, .ps and .pdf