Analysis of Operators and Number Theory

The group’s research interests in operator analysis fall into four main areas: operator analysis in the context of hyperholomorphic functions, Toeplitz operators, spectral theory of Schrödinger operators on geometrically non-trivial domains, and approximation theory. In the latter area, the group also studies problems related to neural network approximation, including polynomial and wavelet approximations. Many of these projects lie at the intersection of operator theory, approximation theory, and models for linear systems in signal processing. Research in number theory focuses primarily on Diophantine approximation and continued fractions.

Research Teams and Staff Involved:

  • Research team coordinator: doc. Baruch Schneider, Ph.D.
  • Jaroslav Hancl, Ladislav Misik, Mohammad Ayman Mursaleen, Diana Schneiderová, Ondřej Turek

Významné projekty za posledních 5 let:

  • NAWA, PS-ZHR-SN, „The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks“, 2022-2024

Major projects over the last five years:

  • Barseghyan, D., Bernstein, S., Schneider, B., Zimmermann, M. L., Magnetic Dirichlet Laplacian in curved waveguides. Opuscula Math. 2025, 45(3), pp. 293-305.
  • Schneider, B., Schneiderová, D., Zhang, Y., Optimization of Robin Laplacian eigenvalue with indefinite weight in spherical shell. Math. Methods Appl. Sci. 2025, No. 48, pp. 6586-6591.
  • Barseghyan, D., Bory-Reyes, J., Schneider, B., Three-dimensional magnetic Schrödinger operator with the potential supported in a tube. Ann. Funct. Anal. 2025, 16(4), No. 76.
  • Mursaleen, M. A., Quadratic function preserving wavelet type Baskakov operators for enhanced function approximation. Comput. Appl. Math. 2025, 44(8), No. 395.
  • Mursaleen, M. A., Alshaban, E., Nasiruzzaman, M., Shape preserving approximation properties to family of α-Bernstein shifted knot operators. J. Inequal. Appl. 2025, 2025(1), No. 107.
  • Mišík, L., Tóth, J.T., Maldistributed sequences in metric spaces. J. Math. Anal. Appl. 2025, 541(2), No. 128667.
  • Bory-Reyes, J., Barseghyan, D., Schneider, B. Magnetic Schroedinger operator with the potential supported in a curved two-dimensional strip. Mediterr. J. Math. 2024, 21(3), pp. 1-15.
  • Alpay, D., Cerejeiras, P., Kaehler, U., Schneider, B., q-rational functions and interpolation with complete Nevanlinna-Pick kernels. Integral Equations Operator Theory. 2024, 96(4), No 27.
  • Hančl, J., Nair, R., On a theorem of Borel on diophantine approximation. Ramanujan J. 2024, 65, 897-915.
  • Goyeneche, D., Bruzda, W., Turek, O., Alsina, D., Zyczkowski, K. Local hidden variable values without optimization procedures. Quantum. 2023, 7, No. 911.

Updated: 04. 06. 2026