Papers:
| 59. | with J. Prochno and M. Sonnleitner | |
| Entropy numbers of finite-dimensional Lorentz space embeddings | ||
| submitted, available at arXiv | ||
| 58. | with J. Haškovec | |
| Robust network formation with biological applications | ||
| Networks and Heterogeneous Media 19(2) (2024), 771-799, available at arXiv | ||
| 57. | with M. Trodler and J. Volec | |
| A tight lower bound on the minimal dispersion | ||
| Eur. J. Combin. 120 (2024), 103945, available at arXiv | ||
| 56. | with C. Schneider | |
| Multivariate Riesz basis of ReLU neural networks | ||
| Appl. Comput. Harmonic Anal. 68 (2024), 101605, available at arXiv | ||
| 55. | with D. Krieg | |
| New lower bounds for the integration of periodic functions | ||
| J. Fourier Anal. Appl. 29 (2023), 41, available at arXiv | ||
| 54. | with H. Kempka and C. Schneider | |
| Path regularity of Brownian motion and Brownian sheet | ||
| Constr. Appr. 59 (2024), 485–539, available at arXiv | ||
| 53. | with A. Hinrichs, D. Krieg, and E. Novak | |
| Lower bounds for integration and recovery in L2 | ||
| J. Compl. (72), October 2022, 101662, available at arXiv | ||
| 52. | with A. Hinrichs and J. Prochno | |
| Gelfand numbers of embeddings of Schatten classes | ||
| Math. Ann. 380 (2021), 1563–1593, available at arXiv | ||
| 51. | with A. Hinrichs, D. Krieg, and E. Novak | |
| Lower bounds for the error of quadrature formulas for Hilbert spaces | ||
| J. Compl. (65), August 2021, 101544, 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 | ||
| Algorithmica 84 (2022), 1897-1915, 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 | ||
| Information and Inference: a Journal of the IMA, 10(2), June 2021, 625-695, available at arXiv | ||
| 45. | with M. Kossaczka | |
| Entropy numbers of finite-dimensional embeddings | ||
| Expositiones Mathematicae 38(3) (2020), 319-336, available at arXiv | ||
| 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 | ||
| 43. | with M. Ullrich | |
| An upper bound on the minimal dispersion | ||
| J. Compl. 45 (2018), 120-126, available at arXiv | ||
| 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 | ||
| 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 | ||
| 40. | with H. F. Goncalves and H. Kempka | |
| Franke-Jawerth embeddings for Besov and Triebel-Lizorkin spaces with variable exponents | ||
| to appear in Ann. Acad. Sci. Fenn. Math., available at arXiv | ||
| 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 | ||
| 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 | ||
| 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 | ||
| 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 | ||
| 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 | ||
| 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