Based on the Riesz potential, S. Samko and coworkers studied the fractional integro-
differentiation of functions of many variables which is a fractional power of the Laplace …

The aim of the paper is to construct the fundamental solution of an arbitrary complex power
of the Dirac operator, these powers being defined as convolution operators with a kernel …

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 …

This work covers three mathematical analysis domains: Continuous Wavelet Transform,
Fourier Transform and Clifford Analysis, and consists of three parts in which these domains …

Possibilities for defining the radial derivative of the delta distribution δ (x) δ (x ̲) in the
setting of spherical coordinates are explored. This leads to the introduction of a new class of …

In recent papers by Brackx, Delanghe and Sommen, some fundamental higher dimensional
distributions have been reconsidered in the framework of Clifford analysis, eventually …

Expressing distributions in Euclidean space in terms of spherical coordinates gives rise to
an alternative class of continuous linear functionals, termed signumdistributions, acting on …

In Brackx et al., 2004 (F. Brackx, R. Delanghe and F. Sommen (2004). Spherical means and
distributions in Clifford analysis. In: Tao Qian, Thomas Hempfling, Alan McIntosch and Frank …

Two specific families of distributions in harmonic and Clifford analysis are further studied
through a spherical co-ordinates approach. In particular actions involving spherical co …

In this paper a new method for constructing Clifford algebra-valued orthogonal polynomials
in Euclidean space is presented. In earlier research, only scalar-valued weight functions …