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On the radial derivative of the delta distribution

Fred Brackx UGent, Franciscus Sommen UGent and Jasson Vindas Diaz UGent (2017) COMPLEX ANALYSIS AND OPERATOR THEORY. 11(5). p.1035-1057
abstract
Possibilities for defining the radial derivative of the delta distribution $\delta(\ux)$ 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 $\delta(\ux)$ 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 $\mR^m$.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Delta distribution, Radial derivative
journal title
COMPLEX ANALYSIS AND OPERATOR THEORY
Complex Anal. Oper. Theory
volume
11
issue
5
pages
1035 - 1057
ISSN
1661-8254
1661-8262
DOI
10.1007/s11785-017-0638-8
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8521566
handle
http://hdl.handle.net/1854/LU-8521566
date created
2017-05-29 17:43:32
date last changed
2017-06-08 07:56:24
@article{8521566,
  abstract     = {Possibilities for defining the radial derivative of the delta distribution \${\textbackslash}delta({\textbackslash}ux)\$ 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 \${\textbackslash}delta({\textbackslash}ux)\$ 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 \${\textbackslash}mR\^{ }m\$.},
  author       = {Brackx, Fred and Sommen, Franciscus and Vindas Diaz, Jasson},
  issn         = {1661-8254},
  journal      = {COMPLEX ANALYSIS AND OPERATOR THEORY},
  keyword      = {Delta distribution,Radial derivative},
  language     = {eng},
  number       = {5},
  pages        = {1035--1057},
  title        = {On the radial derivative of the delta distribution},
  url          = {http://dx.doi.org/10.1007/s11785-017-0638-8},
  volume       = {11},
  year         = {2017},
}

Chicago
Brackx, Fred, Franciscus Sommen, and Jasson Vindas Diaz. 2017. “On the Radial Derivative of the Delta Distribution.” Complex Analysis and Operator Theory 11 (5): 1035–1057.
APA
Brackx, Fred, Sommen, F., & Vindas Diaz, J. (2017). On the radial derivative of the delta distribution. COMPLEX ANALYSIS AND OPERATOR THEORY, 11(5), 1035–1057.
Vancouver
1.
Brackx F, Sommen F, Vindas Diaz J. On the radial derivative of the delta distribution. COMPLEX ANALYSIS AND OPERATOR THEORY. 2017;11(5):1035–57.
MLA
Brackx, Fred, Franciscus Sommen, and Jasson Vindas Diaz. “On the Radial Derivative of the Delta Distribution.” COMPLEX ANALYSIS AND OPERATOR THEORY 11.5 (2017): 1035–1057. Print.