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On the radial derivative of the delta distribution

Fred Brackx (UGent) , Franciscus Sommen (UGent) and Jasson Vindas Diaz (UGent)
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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.
Keywords
Delta distribution, Radial derivative, CLIFFORD ANALYSIS

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Citation

Please use this url to cite or link to this publication:

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.
@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},
}

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