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Twisted plane wave expansions using hypercomplex methods

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Abstract
The purpose of this paper is to derive various representations of the Dirac delta distribution, including a Bony-type twisted Radon decomposition, from boundary values of monogenic functions. This leads to a new and simpler approach based on the properties of the analogue of the Cauchy kernel in the context of monogenic functions.
Keywords
plane wave expansion, monogenic functions, regular functions of a quaternionic variable, delta distribution

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

Chicago
Colombo, Fabrizio, Irene Sabadini, Franciscus Sommen, and Daniele Struppa. 2014. “Twisted Plane Wave Expansions Using Hypercomplex Methods.” Publications of the Research Institute for Mathematical Sciences 50 (1): 1–18.
APA
Colombo, F., Sabadini, I., Sommen, F., & Struppa, D. (2014). Twisted plane wave expansions using hypercomplex methods. PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 50(1), 1–18.
Vancouver
1.
Colombo F, Sabadini I, Sommen F, Struppa D. Twisted plane wave expansions using hypercomplex methods. PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES. 2014;50(1):1–18.
MLA
Colombo, Fabrizio, Irene Sabadini, Franciscus Sommen, et al. “Twisted Plane Wave Expansions Using Hypercomplex Methods.” PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 50.1 (2014): 1–18. Print.
@article{4426058,
  abstract     = {The purpose of this paper is to derive various representations of the Dirac delta distribution, including a Bony-type twisted Radon decomposition, from boundary values of monogenic functions. This leads to a new and simpler approach based on the properties of the analogue of the Cauchy kernel in the context of monogenic functions.},
  author       = {Colombo, Fabrizio and Sabadini, Irene and Sommen, Franciscus and Struppa, Daniele},
  issn         = {0034-5318},
  journal      = {PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES},
  language     = {eng},
  number       = {1},
  pages        = {1--18},
  title        = {Twisted plane wave expansions using hypercomplex methods},
  url          = {http://dx.doi.org/10.4171/PRIMS/123},
  volume       = {50},
  year         = {2014},
}

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