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- Fred Brackx, Nele De Schepper, Frank Sommen
- Journal of Mathematical Imaging and Vision
- 2006

- Fred Brackx, Bram De Knock, Hennie De Schepper
- Int. J. Math. Mathematical Sciences
- 2006

Two specific generalizations of the multidimensional Hilbert transform in Clifford analysis are constructed. It is shown that though in each of these generalizations some traditional properties of the Hilbert transform are inevitably lost, new bounded singular operators emerge on Hilbert or Sobolev spaces of L 2-functions

- Fred Brackx, Bram De Knock, Hennie De Schepper
- Geometric Algebra Computing
- 2010

- Fred Brackx, Ernst Hairer, +7 authors Alexandre Morin
- 2011

- Fred Brackx, Nele De Schepper, Frank Sommen
- Geometric Algebra Computing
- 2010

In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that fixed vector. For this Fourier kernel we now substitute a new Clifford-Fourier kernel such that, again… (More)

- Fred Brackx, Nele De Schepper, Frank Sommen
- Journal of Approximation Theory
- 2005

- Muhammad Yasir Qadri, Fred Brackx, +4 authors Wenhao Ma
- 2015

- Fred Brackx, Nele De Schepper, Frank Sommen
- Int. J. Math. Mathematical Sciences
- 2004

A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clif-ford algebra-valued functions. The method consists in transforming the… (More)

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