List of publications
In preparation
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The fractional Clifford-Fourier transform, currently approx. 15 pages.
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Fourier transform in discrete Clifford analysis, currently approx. 20 pages.
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Conformal invariance of the super Dirac operator, currently approx. 10 pages.
Preprints
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H. De Bie, B. Orsted, P. Somberg and V. Soucek, The Clifford deformation of the Hermite semigroup, arXiv:1101.5551, 27 pages.
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H. De Bie, P. Somberg and V. Soucek, The Howe duality and polynomial solutions for the symplectic Dirac operator, arXiv:1002.1053, 11 pages.
(A1) Papers in journals included in ISI Web of Science
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H. De Bie, D. Struppa, A. Vajiac and M. Vajiac, The Cauchy-Kowalewski product for bicomplex holomorpic functions, accepted for publication in Math. Nachrichten.
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K. Coulembier and H. De Bie , Hilbert space for quantum mechanics on superspace, arXiv:1101.4820, 30 pages. Accepted in J. Math. Phys.
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H. De Bie, B. Orsted, P. Somberg and V. Soucek, Dunkl operators and a family of realizations of osp(1|2), arXiv:0911.4725, 28 pages, accepted in Trans. Amer. Math. Soc.
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K. Coulembier, H. De Bie and F. Sommen, Orthogonality of Hermite polynomials in superspace and Mehler type formulae, arXiv:1002.1118, 43 pages, accepted in Proc. London Math. Soc.
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H. De Bie, N. De Schepper and F. Sommen, The class of Clifford-Fourier transforms, accepted in J. Fourier Anal. Appl., 34 pages, arXiv:1101.1793.
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H. De Bie and N. De Schepper, Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator, accepted in Bulletin of the BMS.
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H. De Bie and Y. Xu, On the Clifford-Fourier transform, Int. Math. Res. Notices (2011), doi: 10.1093/imrn/rnq288, 41 pages.
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K. Coulembier, H. De Bie and F. Sommen, Orthosymplectically invariant functions in superspace, 23 pages, J. Math. Phys. 51 (2010) 083504, 23 pages.
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K. Coulembier, H. De Bie and F. Sommen, Integration in superspace using distribution theory, J. Phys. A: Math. Theor. 42 (2009) 395206 (23pp).
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H. De Bie, F. Sommen, A Cauchy integral formula in superspace, Bull. London Math. Soc. 41 (2009) 709-722.
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H. De Bie, D. Eelbode and F. Sommen, Spherical harmonics and integration in superspace II, J. Phys. A: Math. Theor. 42 (2009) 245204 (18pp).
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H. De Bie, An alternative definition of the Hermite polynomials related to the Dunkl Laplacian, SIGMA 4 (2008), 093, 11 pages.
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H. De Bie, Schrödinger equation with delta potential in superspace, Phys. Lett. A 372 (2008), 4350-4352.
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H. De Bie, Fourier transform and related integral transforms in superspace, J. Math. Anal. Appl. 345 (2008), 147-164.
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H. De Bie, F. Sommen, Fundamental solutions for the super Laplace and Dirac operators and all their natural powers, J. Math. Anal. Appl. 338 (2008), 1320–1328
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H. De Bie, F. Sommen, Hermite and Gegenbauer polynomials in superspace using Clifford analysis, J. Phys. A: Math. Theor. 40 (2007), 10441-10456.
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H. De Bie, F. Sommen, Spherical harmonics and integration in superspace, J. Phys. A: Math. Theor. 40 (2007), 7193-7212.
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H. De Bie, F. Sommen, A Clifford analysis approach to superspace, Ann. Physics. 322 (2007), 2978–2993.
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H. De Bie, F. Sommen, Correct rules for Clifford calculus on superspace, Adv. appl. Clifford alg. 17 (2007), 357–382.
(C) Other publications
(C1) Papers in proceedings of scientific congresses, not included in section (A)
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K. Coulembier, H. De Bie and F. Sommen, Harmonic and monogenic functions in superspace. In ''Hypercomplex Analysis and Applications'', Trends in Mathematics, Birkhauser, pp. 29-41.
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H. De Bie, F. Sommen, Vector and bivector Fourier transforms in Clifford analysis, In "18th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering". K. Gürlebeck and C. Könke (eds.), Weimar, Germany, 07-09 July 2009, 11 pages.
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H. De Bie, F. Sommen, Fischer decompositions in superspace. In "Function spaces in complex and Clifford analysis". National University Publishers Hanoi, 2008, pp. 170-188.
