On the radial derivative of the delta distribution

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 ${\mathbb{R}}^m$.

18 pages

References in corpus (1)

• Rotation invariant ultradistributions

Cited by in corpus (2)

• Cartesian and spherical multipole expansions in anisotropic media
• Distributions in spaces with thick submanifolds