Prof. Dr. Sören Kraußhar

SK 1

Lehrgebäude 2 / Raum 109b

soeren.krausshar(at)uni-erfurt.de

Current Research interests:

  • Dirac and Laplace operator on manifolds
  • Complex and hypercomplex analysis
  • Slice monogenic functions
  • Harmonic and Hypercomplex automorphic forms
  • Parabolic partial differential equations
    • Stokes- and Navier-Stokes
    • Magnetohydrodynamic equations
    • Heat- and Schrödinger type equations
  • fractional differential and integral calculus
  • Special functions
  • Non-commuative geometry
  • Non-abelian gauge theories

A complete information about research activities of the Chair of Mathematics can be found on the web-page.

Complete list of publications (PDF)

International peer reviewed publications of R.S. Kraußhar (last 6 years)

  1. R.S. Kraußhar, A. Legatiuk, D. Legatiuk, Application of the Weyl calculus perspective on discrete octonionic analysis in bounded domains, Complex Analysis and Operator Theory, 19(2), 2025.
  2. R.S. Kraußhar, M. Ferreira, N. Vieira, M.M. Rodrigues, The Teodorescu and the Π-operator in octonionic analysis and some applications, Journal of Geometry and Physics, 206, 2024.
  3. N. Vieira, M. Ferreira, M.M. Rodrigues, R.S. Kraußhar, Hypercomplex operator calculus for the fractional Helmholtz equation, Mathematical Methods in the Applied Sciences, 47(14), 2024.
  4. P. Cerejeiras, U. Kähler, R.S. Kraußhar, Variational principles in quaternionic analysis with applications to the stationary MHD equations, Complex Analysis and Operator Theory, 18(3), 2024.
  5. R.S. Kraußhar: Recent and new results on octonionic Bergman and Szegö kernels, Mathematical Methods in the Applied Sciences, 47(10), 2024.
  6. F. Colombo, R.S. Kraußhar and I. Sabadini: Octonionic monogenic and slice monogenic Hardy and Bergman spaces, Forum Mathematicum, 36(4), 2024.
  7. F. Colombo, R.S. Kraußhar, S. Pinton and I. Sabadini: Entire monogenic functions of given proximate order and continuous homomorphisms, Mediterranean Journal of Mathematics, 21(2), 2024.
  8. R.S. Kraußhar, D. Legatiuk, Cauchy formulae and Hardy spaces in discrete octonionic analysis, Complex Analysis and Operator Theory, 18(1), 2024.
  9. F. Colombo, R.S. Kraußhar, I. Sabadini and Y. Simsek: On the generating functions and special functions associated with superoscillations, Discrete Applied Mathematics, 340, pp. 215-227, 2023.
  10. R.S. Kraußhar, A. Legatiuk and D. Legatiuk: Towards discrete octonionic analysis. In: V. Vasilyev (Ed.), Differential Equations, Mathematical Modeling and Computational Algorithms, Springer, 2023.
  11. R.S. Kraußhar, D. Legatiuk, B. Schneider and T. Truong: A Dynamic Derivative for Fuzzy-Valued Functions, accepted for publication (2022) in American Institute of Physics Conference Proceedings (20th International Conference on Numerical and Applied Mathematics ICNAAM 2022), 4 pages.
  12. R.S. Kraußhar: The Cauchy transform and Kerzman-Stein Theory revisited in the octonionic monogenic setting, accepted for publication (2022) in American Institute of Physics Conference Proceedings (20th International Conference on Numerical and Applied Mathematics ICNAAM 2022), 4 pages.
  13. F. Colombo, R.S. Kraußhar and I. Sabadini: Slice-monogenic theta series, to appear in Indiana University Journal of Mathematics, in press (2022),  28 pages, Preprint available on: https://www.mate.polimi.it/biblioteca/add/quaderni/ qdd234.pdf  
  14. R.S. Kraußhar and A. Perotti: Eigenvalue problems for slice functions, Annali di Matematica Pura ed Applicata 201 (2022), 2519–2548.
  15. R.S. Kraußhar: Recent and new results on octonionic Bergman and Szegö kernels, to appear in Mathematical Methods in the Applied Sciences, in press, accepted in 2021, 14 pages. https://doi.org/10.1002/mma.7316
  16. D. Constales and R.S. Kraußhar: Octonionic Kerzman-Stein operators, Complex Analysis and Operator Theory 15 No.6  Paper No. 104 (2021), 23 pages.
  17. R.S. Kraußhar: Function Theories in Cayley-Dickson algebras and Number Theory, Milan Journal of Mathematics 89 No.1 (2021), 26 pages.
  18. F. Colombo, R.S. Kraußhar and I. Sabadini: Symmetries of slice monogenic functions, Journal of Non-Commutative Geometry 14 No. 3 (2020), 1075-1106.
  19. R.S. Kraußhar: Differential Topological Aspects in Octonionic Monogenic Function Theory, Advances in Applied Clifford Algebras 30 No. 4 Paper No. 51 (2020), 25 pages.
  20. R.S. Kraußhar. Conformal Mappings Revisited in the Octonions and Clifford Algebras in Arbitrary Dimension, Advances in Applied Clifford Algebras 30 No. 3 Paper No. 36 (2020), 14 pages.
  21. K. Diki, R.S. Kraußhar and I. Sabadini: On the Bargmann-Fock-Fueter and Bergman Fueter integral transforms, Journal of Mathematical Physics 60 No. 8:083506 (2019), 29 pages.
  22. M. Ferreira, R.S. Kraußhar, M.M. Rodrigues and N. Vieira: A higher dimensional fractional Borel-Pompeiu formula and a related hypercomplex fractional operator calculus, Mathematical Methods in the Applied Sciences 42 No. 10 (2019), 3633-3653.