Professional orientation: mathematical analysis, potential theory, Clifford analysis

Papers

  1. R. Lávička, The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces, Comment. Math. Univ. Carolinae 39,1 (1998), 115-135.
  2. R. Lávička, The limit points of arithmetic means of sequences in Banach spaces, Comment. Math. Univ. Carolinae 41,1 (2000), 97-106.
  3. R. Lávička, A generalization of Fueter's monogenic functions to fine domains, Rend. Circ. Mat. di Palermo (2) Suppl. 79 (2006), 129-138.
  4. R. Lávička, A.G. O'Farrell and I. Short, Reversible maps in the group of quaternionic Möbius transformations, Math. Proc. Camb. Phil. Soc. 143 (2007), 57-69.
  5. R. Lávička, Finely differentiable monogenic functions, Arch. Math.(Brno) 42 (2006), Suppl., 301-305.
  6. R. Lávička, A remark on fine differentiability, Adv. appl. Clifford alg. 17 (2007), 549-554.
  7. R. Lávička, A generalization of monogenic functions to fine domains, Adv. appl. Clifford alg. 18 (2008), 865-874.
  8. R. Lávička, Finely continuously differentiable functions, Expo. Math. 26 (2008), 353-363.
  9. R. Lávička, Examples of finely monogenic functions, In: ICNAAM 2008, Psalidi, Kos (Greece), 16-20 September 2008", ed. T. E. Simos, G. Psihoyios, Ch. Tsitouras, AIP Conf. Proc. 1048 (2008) (678), American Institute of Physics, Melville, New York, 2008, pp. 678-681.
  10. R. Lávička, On the Structure of Monogenic Multi-Vector Valued Polynomials, In: ICNAAM 2009, Rethymno, Crete, Greece, 18-22 September 2009 (eds. T. E. simos, G. Psihoyios and Ch. Tsitouras), AIP Conf. Proc. 1168 (2009)(793), pp. 793-796.
  11. R. Delanghe, R. Lávička and V. Souček, The Howe duality for Hodge systems, In: Proceedings of 18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering (ed. K. Gürlebeck and C. Könke), Bauhaus-Universität Weimar, Weimar, 2009.
  12. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Fischer decompositions of kernels of Hermitean Dirac operators, In: ICNAAM 2010, Rhodes, Greece, 2010 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1281 (2010), pp. 1484-1487.
  13. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Gel'fand-Tsetlin procedure for the construction of orthogonal bases in Hermitean Clifford analysis, In: ICNAAM 2010, Rhodes, Greece, 2010 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1281 (2010), pp. 1508-1511.
  14. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Orthogonal basis of Hermitean monogenic polynomials: an explicit construction in complex dimension 2, In: ICNAAM 2010, Rhodes, Greece, 2010 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1281 (2010), pp. 1451-1454.
  15. R. Delanghe, R. Lávička and V. Souček, On polynomial solutions of generalized Moisil-Théodoresco systems and Hodge systems, Adv. appl. Clifford alg. 21 (2011), 521–530. See also arXiv:0908.0842v2.
  16. R. Lávička, The Fischer Decomposition for the H-action and Its Applications, In: Hypercomplex analysis and applications, I. Sabadini and F. Sommen (eds.), Trends in Mathematics, Springer Basel AG, 2011, pp. 139-148. See also arXiv:1002.0527v1.
  17. R. Lávička, Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3, Arch. Math.(Brno) 46 (2010) (5), 339-349. See also arXiv:1003.5587v1.
  18. F. Brackx, H. De Schepper, R. Lávička and V. Souček, The Cauchy- Kovalevskaya Extension Theorem in Hermitean Clifford Analysis, J. Math. Anal. Appl. 381 (2011), 649–660.
  19. R. Lávička, V. Souček and P. Van Lancker, Orthogonal basis for spherical monogenics by step two branching, Ann. Glob. Anal. Geom. 41 (2012) (2), 161-186. See also arXiv:1010.1620v1.
  20. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Gelfand-Tsetlin Bases of Orthogonal Polynomials in Hermitean Clifford Analysis, Math. Methods Appl. Sci. 34 (2011), 2167-2180. See also arXiv:1102.4211v1.
  21. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Conjugate harmonic pairs in Hermitean Clifford analysis, In: Proc. of ICCA9, K. Gürlebeck (ed.) Weimar, Germany, 15–20 July 2011.
  22. S. Bock, K. Gürlebeck, R. Lávička and V. Souček, The Gelfand-Tsetlin bases for spherical monogenics in dimension 3, arXiv:1010.1615v2 [math.CV], 2010, to appear in Rev. Mat. Iberoamericana
  23. R. Delanghe, R. Lávička and V. Souček, The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces, Math. Meth. Appl. Sci. 35 (2012), 10–16. See also arXiv:1012.4994v1.
  24. R. Delanghe, R. Lávička and V. Souček, The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces, Math. Meth. Appl. Sci. (2012) DOI: 10.1002/mma.1563. See also arXiv:1012.4998v1.
  25. R. Lávička, Generalized Appell property for the Riesz system in dimension 3, In: ICNAAM 2011, Halkidiki, Greece, 2011 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1389 (2011), pp. 291-294.
  26. R. Lávička, Complete orthogonal Appell systems for spherical monogenics, Complex Anal. Oper. Theory 6 (2012) (2), 477–489. See also arXiv:1106.2970v2 [math.CV], 2011.
  27. F. Brackx, H. De Schepper, R. Lávička and V. Souček, On primitives and conjugate harmonic pairs in Hermitean Clifford analysis, submitted.
  28. R. Lávička, Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces, arXiv:1111.0974v1 [math.CV], 2011, submitted.

Monograph

  1. J. Bureš, R. Lávička and V. Souček, Elements of Quaternionic Analysis and Radon Transform, Textos de Matematica, vol. 42, Universidade de Coimbra, Coimbra, 2009 (vi+72 pages, 100 printed copies).

Theses

  1. R. Lávička, Laplacians in Hilbert spaces and sequences in Banach spaces, PhD thesis, Faculty of Mathematics and Physics, Charles University, Prague, 1998.
  2. R. Lávička, Laplaceovy operátory na Hilbertově prostoru (in Czech), diploma thesis, Faculty of Mathematics and Physics, Charles University, Prague, 1995.