Universität Erfurt

Prof. Dr. Sören Kraußhar

Prof. Dr. Sören Kraußhar

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

Complete list of publications (PDF)

 

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

 

  1. R.S. Kraußhar: Conformal mappings revisited in the octonions and Clifford algebras of arbitrary dimension, submitted for publication (2019) (12 pages).
  2. R.S. Kraußhar: Function Theories in Cayley-Dickson algebras and Number Theory, submitted for publication (2019) (19 pages) Online available: http://arxiv.org/abs/1912.01351
  3. F. Colombo, R.S. Kraußhar and I. Sabadini: Symmetries of slice monogenic functions, accepted for publication (2019), to appear in: Journal of Non-Commutative Geometry (24 pages)
  4. 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), DOI: 10.1063/1.5094384  (26 pages)
  5. 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.  https://doi.org/10.1002/mma.5602
  6. P. Cerejeiras, U. Kähler and R.S. Kraußhar: Applications of parabolic Dirac operators to the instationary viscous MHD equations on conformally flat manifolds, in: Topics in Clifford Analysis, [eds. S. Bernstein], Trends in Mathematics, Birkhäuser, Basel, 2019, 173-190. [ISBN 978-3-030-23854-4]  Online available on: https://arxiv.org/abs/1804.09551 
  7. R.S. Kraußhar: Automorphic Forms and Dirac Operators and Confomally Flat Manifolds, in: Topics in Clifford Analysis, [eds. S. Bernstein], Trends in Mathematics, Birkhäuser, Basel, 2019, 331-345. [ISBN 978-3-030-23854-4]   Online available on: http://arxiv.org/abs/1804.04387
  8. P. Cerejeiras, U. Kähler and R.S. Kraußhar: Some applications of parabolic Dirac operators to the instationary Navier-Stokes problem on conformally flat cylinders and tori in R3, In: Clifford Analysis and Related Topics CART 2014, [eds. P. Cerejeiras, C. Nolder, J. Ryan, J. Vanegas]. Springer Proceedings in Mathematics & Statistics 260, 19-37, Springer, Cham, 2018, 19-37.  [ISBN 978-3-030-00047-9/hbk; 978-3-030-00049-3/ebook]. Online available on: http://arxiv.org/abs/1804.01767   
  9. R. De Almeida und R.S. Kraußhar: Wiman-Valiron theory for higher dimensional polynomial Cauchy-Riemann equations, Mathematical Methods in the Applied Sciences 41 No. 1 (2018), 15-27.  
  10. R.S. Kraußhar, M. Rodrigues und N. Vieira: Maximum principle and parabolic inequalities for the regularized Schrödinger operator, Results Math. 69 No.1-2 (2016), 49-68.
  11. R.S. Kraußhar, M. Rodrigues und N. Vieira: Time-dependent operators on some non-orientable projective orbifolds, Mathematical Methods in the Applied Sciences 38 No. 18 (2016), 5305-5319
  12. R. De Almeida und R.S. Kraußhar: Generalized growth orders for polymonogenic functions and related inequalities, Complex Analysis an Operator Theory 10 No.2 (2016), 233-250.
  13. R.S. Kraußhar: Dirac and Laplace operators on some non-orientable conformally flat manifolds, Journal of Mathematical Analysis and its Applications 427 No. 2 (2015), 669-685.
  14. R. De Almeida und R.S. Kraußhar: Basics on growth orders of polymonogenic functions, Complex Variables and Elliptic Equations 60 No. 11, (2015), 1480-1504.
  15. R.S. Kraußhar und J. Tolksdorf: Applications of hypercomplex automorphic forms in Yang-Mills gauge theories, Complex Analysis and Operator theory 9 (2015), 431-444.
  16. D. Grob und R.S. Kraußhar: A Selberg trace formula for hypercomplex analytic cusp forms, Journal of Number Theory 148 (2015), 398-428.
  17. R.S. Kraußhar, M. Rodrigues und N. Vieira: Hodge type decomposition for time dependent first order parabolic operators with non-constant coefficients: the variable exponent case, Milan Journal of Mathematics 82 (2014), 407-422.
  18. R.S. Kraußhar, M.M. Rodrigues und N. Vieira: Hodge decomposition for some first order time dependent parabolic operators with non-constant coefficients, Annali di Matematica Pura ed Applicata 193 (2014), 1807-1821.
  19. R.S. Kraußhar: Applications of the quaternionic calculus to the convective stationary MHD equations in Rn, Advances in Applied Clifford Algebras 24 No. 4 (2014), 1047-1058.
  20. R.S. Kraußhar, M.M. Rodrigues und N. Vieira: The Schrödinger semigroup on some flat and non flat manifolds, Complex Analysis and Operator Theory 8 No. 2 (2014), 461-484.
  21. R.S. Kraußhar: The Klein-Gordon operator on Möbius strip domains and the Klein bottle in Rn, Mathematical Physics, Analysis and Geometry 16 (2013), 363-379.
  22. D. Constales, R. De Almeida und R.S. Kraußhar: The Fourier expansion of the hypermonogenic generalized trigonometric and elliptic functions, J. Number Theory 133 (2013), 1991-2004.
  23. D. Constales, D. Grob und R.S. Kraußhar: A new class of hypercomplex analytic cusp forms, Transactions of the AMS 365 No. 2 (2013), 811-835.
  24. D. Constales, D. Grob, R.S. Kraußhar: On Dirichlet problems of polynomial Dirac equations with boundary conditions, Results in Math. 64 (2013), 193-213. 

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