Abstract
Possibilities for defining the radial derivative of the delta distribution \(\delta (\underline{x})\) in the setting of spherical coordinates are explored. This leads to the introduction of a new class of continuous linear functionals similar to but different from the standard distributions. The radial derivative of \(\delta (\underline{x})\) then belongs to that new class of so-called signumdistributions. It is shown that these signumdistributions obey easy-to-handle calculus rules which are in accordance with those for the standard distributions in \({\mathbb {R}}^m\).
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Acknowledgements
The first author wants to thank Kevin Coulembier, Hendrik De Bie, Hennie De Schepper, and David Eelbode for their interest in and their valuable comments on the topic treated in this paper.
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Communicated by Irene Sabadini.
Dedicated to our co-author Frank on the occasion of his 60th birthday.
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Brackx, F., Sommen, F. & Vindas, J. On the Radial Derivative of the Delta Distribution. Complex Anal. Oper. Theory 11, 1035–1057 (2017). https://doi.org/10.1007/s11785-017-0638-8
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DOI: https://doi.org/10.1007/s11785-017-0638-8