Generalized derivatives of spherical associated homogeneous distributions on Rn
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Full proofs are given of general expressions for the generalized partial derivatives of spherically symmetric associated homogeneous distributions (SAHDs) based on Rn. This work complements earlier work began by Estrada and Kanwal. Special attention is given to the cases when the derivative of the distribution is a singular distribution, being either an analytic continuation or a distributional extension (or regularization). The presented results are useful for the distributional treatment of potential (i.e., time-invariant) problems in n dimensions. © 2009 Elsevier Inc. All rights reserved.
CitationFranssens, G.R. (2009). Generalized derivatives of spherical associated homogeneous distributions on Rn. , Journal of Mathematical Analysis and Applications, Vol. 355, Issue 2, 750-766, DOI: 10.1016/j.jmaa.2009.02.031.