Professional orientation: mathematical analysis, hypercomplex analysis, potential theory

Research papers

    Preprints of my papers are available on arXiv.org.

  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. 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.
  10. R. Lávička, Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3, Arch. Math.(Brno) 46 (2010) (5), 339-349.
  11. 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.
  12. 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.
  13. 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.
  14. S. Bock, K. Gürlebeck, R. Lávička and V. Souček, The Gelfand-Tsetlin bases for spherical monogenics in dimension 3, Rev. Mat. Iberoamericana 28 (2012) (4), 1165-1192.
  15. R. Delanghe, R. Lávička and V. Souček, The Fischer decomposition for Hodge-de Rham systems in Euclidean spaces, Math. Meth. Appl. Sci. 35 (2012) (1), 10–16.
  16. R. Delanghe, R. Lávička and V. Souček, The Gelfand-Tsetlin bases for Hodge-de Rham systems in Euclidean spaces, Math. Meth. Appl. Sci. 35 (2012) (7), 745-757.
  17. R. Lávička, Complete orthogonal Appell systems for spherical monogenics, Complex Anal. Oper. Theory 6 (2012) (2), 477–489.
  18. F. Brackx, H. De Schepper, R. Lávička and V. Souček, On primitives and conjugate harmonic pairs in Hermitian Clifford analysis, Complex Anal. Oper. Theory 7 (2013) (5), 1583-1607.
  19. R. Lávička, Orthogonal Appell bases for Hodge-de Rham systems in Euclidean spaces, Adv. appl. Clifford alg. 23 (2013) (1), 113-124.
  20. P. Cerejeiras, U. Kaehler and R. Lávička, Generating functions for spherical harmonics and spherical monogenics, Adv. appl. Clifford alg. 24 (2014), 995–1004.
  21. F. Brackx, H. De Schepper, D. Eelbode, R. Lávička and V. Souček, Fundaments of Quaternionic Clifford Analysis I: Quaternionic Structure, Adv. appl. Clifford alg. 24 (2014), 955–980.
  22. F. Brackx, H. De Schepper, D. Eelbode, R. Lávička and V. Souček, Fischer Decomposition in Symplectic Harmonic Analysis, Ann. Glob. Anal. Geom. 46 (4) (2014), 409–430.
  23. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Embedding Factors for Branching in Hermitian Clifford Analysis, Complex Anal. Oper. Theory 9 (2015), no. 2, 355–378.
  24. F. Brackx, H. De Schepper and R. Lávička, Generalized Taylor Series in Hermitian Clifford Analysis, J. Math. Anal. Appl. 421 (2015), 1531–1545.
  25. F. Colombo, R. Lávička, I. Sabadini and V. Souček, The Radon transform between monogenic and generalized slice monogenic functions, Math. Ann. 363 (2015), 733-752.
  26. F. Colombo, R. Lávička, I. Sabadini and V. Souček, Monogenic plane waves and the W-functional calculus, Math. Meth. Appl. Sci. 39 (2015), 412-424.
  27. R. Lávička, D. Šmíd, Fischer decomposition for polynomials on superspace, J. Math. Phys. 56, 111704 (2015).
  28. F. Brackx, H. De Schepper, D. Eelbode, R. Lávička and V. Souček, Fundaments of Quaternionic Clifford Analysis II: Splitting of Equations, Complex Var. Elliptic Equ. 62 (2017) (5), 616-641.
  29. F. Brackx, H. De Schepper, D. Eelbode, R. Lávička and V. Souček, Fischer Decomposition for osp(4|2)-monogenics in Quaternionic Clifford Analysis, Math. Meth. Appl. Sci. 39 (2016) (16), 4874-4891.
  30. R. Howe, R. Lávička, S.T. Lee, V. Souček, A reciprocity law and the skew Pieri rule for the symplectic group, J. Math. Phys. 58 , 031702 (2017).
  31. F. Brackx, H. De Schepper, D. Eelbode, R. Lávička and V. Souček, Fischer decomposition for the symplectic group, J. Math. Anal. Appl. 458 (2018), 831-848.
  32. R. Lávička and V. Souček, Fischer decomposition for spinor valued polynomials in several variables, arXiv:1708.01426
  33. F. Brackx, H. De Schepper, R. Lávička and V. Souček, The Cauchy Integral Formula in Hermitian, Quaternionic and osp(4|2) Clifford Analysis, Comput. Methods Funct. Theory 20 (2020), 431–464. https://doi.org/10.1007/s40315-020-00322-z
  34. R. Lávička, V. Souček and W. Wang, General massless field equations for higher spin in dimension 4, Math Meth Appl Sci. 2021, 1- 13. https://doi.org/10.1002/mma.7598
  35. F. Brackx, H. De Schepper, R. Lávička, V. Souček and W. Wang; Fischer Decomposition of Massless Fields for Spin 3/2 in Dimension 4. Adv. Appl. Clifford Algebras 32, 6 (2022). https://doi.org/10.1007/s00006-021-01187-8
  36. R. Lávička, Branching laws for spherical harmonics on superspaces in exceptional cases, arXiv:2306.09047
  37. R. Lávička, V. Souček and W. Wang, Massless field equations for spin 3/2 in dimension 6, arXiv:2311.09728

Articles in Proceedings

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. F. Brackx, H. De Schepper and R. Lávička, Branching of monogenic polynomials, In: ICNAAM 2012, Kos, Greece, 2012 (eds. T.E. Simos, G. Psihoyios, Ch. Tsitouras), AIP Conf. Proc. 1479 (2012), pp. 304-307.
  11. F. Brackx, H. De Schepper, D. Eelbode, R. Lávička and V. Souček, osp(4|2)–monogenicity in Clifford analysis, In: 15th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2015), Costa Ballena, Rota, Cadiz (Spain), 6-10 July 2015, pp. 240-243.
  12. R. Lávička, Separation of variables in the semistable range. In: Bernstein S. (eds) Topics in Clifford Analysis. Trends in Mathematics. Birkhäuser, Cham, 2019, pp 395-403; ISBN 978-3-030-23853-7, https://doi.org/10.1007/978-3-030-23854-4_19
  13. F. Brackx, H. De Schepper, R. Lávička and V. Souček, Cauchy’s Formula in Clifford Analysis: An Overview. In: Bernstein S. (eds) Topics in Clifford Analysis. Trends in Mathematics. Birkhäuser, Cham, 2019, pp 3-23; ISBN 978-3-030-23853-7, https://doi.org/10.1007/978-3-030-23854-4_1

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, Hypercomplex Analysis - Selected Topics, habilitation thesis, Faculty of Mathematics and Physics, Charles University, Prague, 2011.
  2. R. Lávička, Laplacians in Hilbert spaces and sequences in Banach spaces, PhD thesis, Faculty of Mathematics and Physics, Charles University, Prague, 1998.
  3. R. Lávička, Laplaceovy operátory na Hilbertově prostoru (in Czech), diploma thesis, Faculty of Mathematics and Physics, Charles University, Prague, 1995.

My ORCID ID: 0000-0002-5351-3972
My Scopus ID: 18042185300
My Researcher ID: O-4444-2017

Citations to my articles (Google Scholar)