A Cauchy-Pompeiu Representation Formula Using Dirac Operator and its Applications in Some Piecewise Constant Structure Relations

Antonio Di Teodoro, Adrián Infante

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In the present paper we use the piecewise constant structure relations of a Clifford algebra in order to obtain a Cauchy-Pompeiu representation for D - λ and D + λ operators, with these formulas we construct a distributional solutions for the equations that involves these operators with arbitrary right hand side. We also present an example where we build an integral representation for combinations of these operators.

Original languageEnglish
Pages (from-to)323-337
Number of pages15
JournalAdvances in Applied Clifford Algebras
Volume23
Issue number2
DOIs
StatePublished - Jun 2013
Externally publishedYes

Keywords

  • Cauchy-Pompeiu formula
  • Clifford analysis
  • Fundamental solution
  • Integral representation
  • Structure relations of Clifford algebra

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