Research Group of Prof. Dr. Kateryna Pozharska

Address:
Institut für Numerische Simulation
Friedrich-Hirzebruch-Allee 7
53115 Bonn
Phone: +49 228 73-2204
Office: FHA7 3.032
E-Mail: ed tod nnob-inu tod sni ta aksrahzopa tod b@foo tod de

Research interests

Approximation, recovery and learning: finding error bounds (both asymptotic and preasymptotic) for recovery of classes and individual functions from incomplete data, as standard (function values, samples) or linear information, when using different algorithms (linear, nonlinear); comparison of efficiency and complexity of decoders (known as information-based complexity).

Discretization: developing methods for construction of exact Marcinkiewicz-Zygmund inequalities, quadrature formulas and tight frames.

Compressed sensing and sparse recovery: developing and investigating data sparsification techniques; recovery of vectors and functions using nonlinear decoders, in particular, rLASSO (square-root least absolute shrinkage and selection operator), OMP (orthogonal matching pursuit), etc.

Teaching

Winter semester 2026/27

See teaching activities of the whole group.

Publications

Journal Papers

  1. Sampling recovery in L_2 and other norms. D. Krieg, K. Pozharska, M. Ullrich, and T. Ullrich. Math. Comput., 96(363):223–253, 2027 (Published online: October 6, 2025). BibTeX DOI
  2. Sampling projections in the uniform norm. D. Krieg, K. Pozharska, M. Ullrich, and T. Ullrich. Journal of Mathematical Analysis and Applications, 553(2):129873, 2026. BibTeX DOI
  3. High-dimensional sparse recovery from function samples – decoders, guarantees and instance optimality. M. Moeller, S. Neumayer, K. Pozharska, T. Sommerfeld, and T. Ullrich. Applied and Computational Harmonic Analysis, pages 101941, 2026. BibTeX DOI
  4. Approximation characteristics of Nikolskii-Besov and Sobolev classes in the space B_{q,1}. K. Pozharska and A. S. Romanyuk. Matematychni Studii, 66:57–70, 2026. BibTeX DOI
  5. Exact discretization, tight frames and recovery via D-optimal designs. F. Bartel, L. Kämmerer, K. Pozharska, M. Schäfer, and T. Ullrich. The SMAI Journal of computational mathematics, 11:607–636, 2025. BibTeX DOI
  6. Estimates for approximation characteristics of Nikol'skii–Besov classes of functions with mixed smoothness in the space B_{q,1}. K. Pozharska and A.S. Romanyuk. Mathematische Nachrichten, 298(9):3114–3134, 2025. BibTeX DOI
  7. Estimates of the characteristics of nonlinear approximation of classes of periodic functions of many variables. K. Pozharska, A.S. Romanyuk, and S.Ya. Yanchenko. Carpathian Mathematical Publications, 17(2):447–460, 2025. BibTeX DOI
  8. Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative. K. Pozharska, A. Romanyuk, and S. Yanchenko. Ukr. Math. J., 76(7):1144–1162, August 2024. BibTeX DOI
  9. The best m-term trigonometric approximations of the classes of periodic functions of one and many variables in the space B_{q,1}. K. Pozharska and A. S. Romanyuk. Res. Math., 32(2):137, 2024. BibTeX DOI
  10. Widths and entropy numbers of the classes of periodic functions of one and several variables in the space B_{q,1}. K. Pozharska, A.S. Romanyuk, and V.S. Romanyuk. Carpathian Mathematical Publications, 16(2):351–366, 2024. BibTeX DOI
  11. Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions. A.S. Romanyuk, V.S. Romanyuk, K. Pozharska, and S.B. Hembarska. Carpathian Mathematical Publications, 15(1):78–94, 2023. BibTeX DOI
  12. A note on sampling recovery of multivariate functions in the uniform norm. K. Pozharska and T. Ullrich. SIAM Journal on Numerical Analysis, 60(3):1363–1384, 2022. BibTeX DOI
  13. On some approximation properties of Gauss-Weierstrass singular operators. O. Shvai and K. Pozharska. J. Math. Sci., 260(5):693–699, 2022. BibTeX DOI
  14. Recovery of continuous functions of two variables from their fourier coefficients known with error. K. Pozharska and A.A. Pozharskyi. Carpathian Mathematical Publications, 13(3):676–686, 2021. BibTeX DOI
  15. Asymptotics of approximation of functions by conjugate Poisson integrals. I.V. Kalchuk, Yu.I. Kharkevych, and K. Pozharska. Carpathian Mathematical Publications, 12(1):138–147, 2020. BibTeX DOI
  16. Asymptotics of approximation of conjugate functions by Poisson integrals. Yu.I. Kharkevych and K. Pozharska. Acta Comment. Univ. Tartu. Math., 22(2):235–243, 2019. BibTeX DOI
  17. Estimates for the entropy numbers of the classes B_{p,\theta }^\Omega of periodic multivariable functions in the uniform metric. K. Pozharska. Ukr. Math. J., 70(9):1439–1455, 2019. BibTeX DOI
  18. Entropy numbers of the Nikol'skii–Besov-type classes of periodic functions of many variables. K. Pozharska. J. Math. Sci., 241(1):64–76, 2019. BibTeX DOI
  19. Estimation of the best bilinear approximations for the classes of (ψ, B)-differentiable periodic multivariable functions. K. Pozharska and (Shvai K.). Ukr. Math. J., 70(4):649–660, 2018. BibTeX DOI
  20. The best M-term trigonometric approximations of the classes of periodic multivariate functions with bounded generalized derivative in the space L_q. K. Pozharska and (Shvai K.). J. Math. Sci., 222(6):750–761, 2017. BibTeX DOI
  21. The best M-term trigonometric approximations of classes of \psi ,\beta -differentiable periodic multivariate functions in the space L_q. K. Pozharska and (Shvai K.). J. Comp. Appl. Math. of the Taras Shevchenko National University of Kyiv, 122(2):83–91, 2016. BibTeX

Proceedings, Series- and Book Contributions

  1. Sampling designs for function recovery – theoretical guarantees, comparison and optimality. M. Moeller, K. Pozharska, and T. Ullrich. In C. Lemieux and B. Feng, editors, Monte Carlo and Quasi-Monte Carlo 2024, 337–356. Cham, 2026. Springer Nature Switzerland. BibTeX
  2. Characteristics of linear and nonlinear approximation of classes of periodic functions of many variables in Lebesgue subspaces. A. Romanyuk, K. Pozharska, and S. Yanchenko. In R. Dmytryshyn, editor, Current trends in analysıs, approximation theory and their applications, chapter 8, pages 236–276. Selcuk University Press, 2026. BibTeX DOI
  3. Estimates of characteristics of nonlinear approximation of classes of periodic functions. K. Pozharska. Transactions of Institute of Mathematics of the NAS of Ukraine, 21(1):149–168, 2025. BibTeX DOI
  4. Best approximations and entropy numbers of the classes of periodic functions of many variables. K. Pozharska. TEMat monográficos, 2:147–150, 2021. BibTeX
  5. Estimates for the best M-term trigonometric approximations of classes L_{\beta ,p}^\psi of periodic multivariable functions in the case of small smoothness in the space L_q. K. Pozharska and (Shvai K.). Transactions of Institute of Mathematics of the NAS of Ukraine, 14(3):293–318, 2017. BibTeX
  6. Estimates of the best orthogonal trigonometric approximations of the generalized multidimensional analogues of the Bernoulli kernels and classes L^\psi _{\beta ,1} in the space L_q. K. Pozharska and (Shvai K.). Transactions of Institute of Mathematics of the NAS of Ukraine, 13(1):300–320, 2016. BibTeX