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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((x) under bar) 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((x) under bar) 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 R-m.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (proceedingsPaper)
publication status
published
subject
keyword
Delta distribution, Radial derivative, CLIFFORD ANALYSIS
journal title
COMPLEX ANALYSIS AND OPERATOR THEORY
Complex Anal. Oper. Theory
volume
11
issue
5
pages
1035 - 1057
conference name
International conference on Past and Future Directions in Hypercomplex and Harmonic Analysis in honor of Frank Sommen's 60th birthday
conference location
Aveiro, Portugal
conference start
2016-03-29
conference end
2016-04-02
Web of Science type
Article; Proceedings Paper
Web of Science id
000402165300005
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
2018-06-02 22:30:18
@article{8521566,
  abstract     = {Possibilities for defining the radial derivative of the delta distribution delta((x) under bar) 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((x) under bar) 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 R-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,CLIFFORD ANALYSIS},
  language     = {eng},
  location     = {Aveiro, Portugal},
  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. Presented at the International conference on Past and Future Directions in Hypercomplex and Harmonic Analysis in honor of Frank Sommen’s 60th birthday.
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.