On the Fourier transform of distributions and differential operators in Clifford analysis
Title:
On the Fourier transform of distributions and differential operators in Clifford analysis
Author:
Brackx, Fred De Schepper, Hennie
Appeared in:
Complex variables and elliptic equations
Paging:
Volume 49 (2004) nr. 15 pages 1079-1091
Year:
2004-12-15
Contents:
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 Sommen (Eds.), Advances in Analysis and Geometry: New Developments Using Clifford Algebra, Trends in Mathematics, pp. 65-96. Birkhauser, Basel.), some fundamental higher dimensional distributions have been reconsidered within the framework of Clifford analysis. Here, the Fourier transforms of these distributions are calculated, revealing a.o. the Fourier symbols of some important translation invariant (convolution) operators, which can be interpreted as members of the considered families. Moreover, these results are the incentive for calculating the Fourier symbols of some differential operators which are at the heart of Clifford analysis, but do not show the property of translation invariance and hence, can no longer be interpreted as convolution operators.
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