Nele De Schepper

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Publications

A1

  1. F. Brackx, N. De Schepper, F. Sommen, The Clifford-Laguerre continuous wavelet transform, Bull. Belg. Math. Soc. Simon Stevin 11 (2004), no. 2, 201--215. link
  2. F. Brackx, N. De Schepper, F. Sommen, The Clifford-Gegenbauer polynomials and the associated continuous wavelet transform, Integral Transforms Spec. Funct. 15 (2004), no. 5, 387--404. doi: 10.1080/10652460410001727536
  3. F. Brackx, N. De Schepper, F. Sommen, Clifford algebra-valued orthogonal polynomials in Euclidean space, J. Approx. Theory 137 (2005), no. 1, 108--122. doi: 10.1016/j.jat.2005.08.004
  4. F. Brackx, N. De Schepper, F. Sommen, The Clifford-Fourier transform, J. Fourier Anal. Appl. 11 (2005), no. 6, 669--681. doi: 10.1007/s00041-005-4079-9
  5. F. Brackx, N. De Schepper, F. Sommen, Clifford-Hermite-monogenic operators, Czechoslovak Math. J. 56(131) (2006), no. 4, 1301--1322. doi: 10.1007/s10587-006-0095-4
  6. F. Brackx, N. De Schepper, F. Sommen, The two-dimensional Clifford-Fourier transform, J. Math. Imaging Vision 26 (2006), no. 1-2, 5--18. doi: 10.1007/s10851-006-3605-y
  7. F. Brackx, N. De Schepper, K.I. Kou, F. Sommen, The Mehler formula for the generalized Clifford-Hermite polynomials, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 4, 697--704. doi: 10.1007/s10114-005-0754-7
  8. F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, Hermitean Clifford-Hermite polynomials, Adv. Appl. Clifford Algebr. 17 (2007), no. 3, 311--330. doi: 10.1007/s00006-007-0032-0
  9. F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, Hermitian Clifford-Hermite wavelets: an alternative approach, Bull. Belg. Math. Soc.-Simon Stevin 15(1) (2008), 87--107. link
  10. F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, Two-index Clifford-Hermite polynomials with applications in wavelet analysis, J. Math. Anal. Appl. 341(1) (2008), 120--130. 10.1016/j.jmaa.2007.10.009
  11. F. Brackx, H. De Schepper, N. De Schepper, D. Eelbode, F. Sommen, Orthogonality of the Generalized Hermitean Clifford-Hermite Polynomials, Int. Transf. Spec. Funct. 19(9-10) (2008), 687--707. doi: 10.1080/10652460802166799
  12. N. De Schepper, The generalized Clifford-Gegenbauer polynomials revisited, Adv. Appl. Clifford Algebras 19(2) (2009), 253--268. doi: 10.1007/s00006-009-0152-9
  13. F. Brackx, N. De Schepper, F. Sommen, The Fourier Transform in Clifford Analysis,. In: P.W. Hawkes (ed.), Adv. Imag. Elect. Phys. 156, Academic Press, San Diego, 2009, 55--201. doi: 10.1016/S1076-5670(08)01402-x 6
  14. F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, Generalized Hermitean Clifford-Hermite Polynomials and the Associated Wavelet Transform, Math. Meth. Appl. Sci. 32(5) (2009), 606--630. doi: 10.1002/mma.1057
  15. F. Brackx, N. De Schepper, F. Sommen, The Clifford-Fourier integral kernel in even dimensional Euclidean space, J. Math. Anal. Appl. 365(2) (2010), 718--728. doi: 10.1016/j.jmaa.2009.12.008
  16. H. De Bie, N. De Schepper, Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator, Bull. Belg. Math. Soc.-Simon Stevin 18(2) (2011), 193--214. link
  17. H. De Bie, N. De Schepper, F. Sommen, The class of Clifford-Fourier transforms, J. Four. Anal. Appl. 17(6) (2011), 1198--1231. doi: 10.1007/s00041-011-9177-2
  18. N. De Schepper, F. Sommen, Closed form of the Fourier-Borel kernel in the framework of Clifford analysis, Results in mathematics, online. doi: 10.1007/s00025-011-0138-5
  19. H. De Bie, N. De Schepper, Fractional Fourier transforms of hypercomplex signals, accepted for publication in Signal, Image and Video Processing, 8 pages.
  20. N. De Schepper, F. Sommen, Cauchy-Kowalevski extensions and monogenic plane waves in Clifford analysis, accepted for publication in a special volume of Adv. Appl. Clifford Algebras in memory of Prof. Jaime Keller, 23 pages.
  21. H. De Bie, N. De Schepper, The fractional Clifford-Fourier transform, Journal of Operator Theory, online. doi: 10.1007/s11785-012-0229-7
  22. N. De Schepper, F. Sommen, Cauchy-Kowalevski extensions and monogenic plane waves using spherical monogenics, submitted to Bulletin of the Brazilian Mathematical Society.

A2

  1. F. Brackx, N. De Schepper, F. Sommen, The higher dimensional Hermite transform: a new approach, Complex Var. Theory Appl. 48 (2003), no. 3, 189--210. doi: 10.1080/0278107031000073579
  2. F. Brackx, N. De Schepper, F. Sommen, The bi-axial Clifford-Hermite continuous wavelet transform, J. Nat. Geom. 24 (2003), no. 1-2, 81--100.
  3. F. Brackx, N. De Schepper, F. Sommen, Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space, Int. J. Math. Math. Sci. 2004, no. 49-52, 2761--2772. doi: 10.1155/S0161171204401045
  4. B. De Knock, N. De Schepper, F. Sommen, Curved Radon transforms and factorization of the Veronese equations in Clifford analysis, Complex Var. Elliptic Equ. 51 (2006), no. 5-6, 511--545. doi: 10.1080/17476930500482556

B2

  1. N. De Schepper and D. Peña Peña, Factorization of the Schrödinger operator and the Riccati equation in the Clifford analysis setting, Liber Amicorum Richard Delanghe: een veelzijdig wiskundige, F. Brackx and H. De Schepper (eds.), Academia Press, Gent, 2005, 69--84. ISBN: 90-382-0853-7
  2. F. Brackx, N. De Schepper, F. Sommen, Metric dependent Clifford analysis with applications to wavelet analysis, Wavelets, multiscale systems and hypercomplex analysis, 17--67, Oper. Theory Adv. Appl., 167, Birkhäuser, Basel, 2006. ISBN 978-3-7643-7587-4
  3. F. Brackx, N. De Schepper, F. Sommen, The Cylindrical Fourier transform. In: E. Bayro-Corrochano and G. Scheuermann (eds.), Geometric algebra computing in engineering and computer science, Springer, London, UK, 2010, 107--119. ISBN 978-1-8499-6107-3

P1

  1. F. Brackx, N. De Schepper, F. Sommen, Clifford-Jacobi polynomials and the associated continuous wavelet transform in Euclidean space, Wavelet analysis and applications, 185--198, Appl. Numer. Harmon. Anal., Birkhäuser, Basel, 2007. ISBN: 978-3-7643-7777-9
  2. F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, The generalized Hermitean Clifford-Hermite continuous wavelet transform, AIP Conference Proceedings Volume 936, Numerical Analysis and Applied Mathematics: International Conference of Numerical Analysis and Applied Mathematics, Corfu (Greece), 16-20 September 2007, Theodore E. Simos, George Psihoyios and Ch. Tsitouras (eds.), 721--725. ISBN: 978-0-7354-0447-2
  3. F. Brackx, N. De Schepper, F. Sommen, The Cylindrical Fourier Spectrum of an L2-basis consisting of Generalized Clifford-Hermite Functions, AIP Conference Proceedings Volume 1048, Numerical Analysis and Applied Mathematics: International Conference of Numerical Analysis and Applied Mathematics, Kos (Greece), 16-20 September 2008, Theodore E. Simos, George Psihoyios and Ch. Tsitouras (eds.), 686--690. ISBN: 978-0-7354-0576-9

C1

  1. F. Brackx, N. De Schepper, F. Sommen, The Hermite Transform in Quaternionic Analysis. In: (digital) Proceedings 16th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, K. Gürlebeck, L. Hempel and C. Könke (eds.), 10-12 June 2003, Bauhaus-Universität Weimar.
  2. F. Brackx, N. De Schepper, F. Sommen, New multivariable polynomials and their associated continuous wavelet transform in the framework of Clifford analysis, Methods of complex and Clifford analysis, 275--294, SAS Int. Publ., Delhi, 2004. ISBN: 81-88296-01-5
  3. F. Brackx, N. De Schepper, F. Sommen, Clifford-Hermite-monogenic operators in the polynomial framework, Methods of complex and Clifford analysis, 239--246, SAS Int. Publ., Delhi, 2004. ISBN: 81-88296-01-5
  4. F. Brackx, N. De Schepper, F. Sommen, Clifford-Hermite and Two-Dimensional Clifford-Gabor Filters for Early Vision. In: (digital) Proceedings 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, K. Gürlebeck and C. Könke (eds.), 12-14 July 2006, Bauhaus-Universität Weimar.
  5. F. Brackx, H. De Schepper, N. De Schepper, F. Sommen, Hermitian Clifford-Hermite Wavelets. In: (digital) Proceedings 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering, K. Gürlebeck and C. Könke (eds.), 12-14 July 2006, Bauhaus-Universität Weimar.
  6. F. Brackx, B. De Knock, H. De Schepper, N. De Schepper, F. Sommen, A new Hilbert transform in Hermitean Clifford analysis. In: L. H. Son and W. Tutschke (eds.), Function Spaces in Complex and Clifford Analysis (Proceedings of the 14th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Hue University, Vietnam, August 01-05, 2006), National University Publishers, Hanoi, 2008, 109--126.
  7. F. Brackx, N. De Schepper, F. Sommen, The Cylindrical Fourier Transform. In: (digital) Proceedings of AGACSE2008.
  8. F. Brackx, N. De Schepper, F. Sommen, The Fourier-Bessel Transform. In: (digital) Proceedings 18th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering, K. Gürlebeck and C. Könke (eds.), 7-9 July 2009, Bauhaus-Universität Weimar.
  9. H. De Bie, N. De Schepper, Translation and convolution in Clifford analysis, submitted for publication in (digital) Proceedings of AGACSE2012.