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arXiv · 1609.09771

On the radial derivative of the delta distribution

Fred Brackx·Frank Sommen·Jasson Vindas
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Abstract

Possibilities for defining the radial derivative of the delta distribution $δ(\underline{x})$ 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 $δ(\underline{x})$ 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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Fred Brackx, Frank Sommen, Jasson Vindas. 2016-09-30. On the radial derivative of the delta distribution. https://doi.org/10.1007/s11785-017-0638-8

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