Cauchy-Green type formulae in Clifford analysis

Author:
John Ryan

Journal:
Trans. Amer. Math. Soc. **347** (1995), 1331-1341

MSC:
Primary 30G35; Secondary 58G99

DOI:
https://doi.org/10.1090/S0002-9947-1995-1249888-8

MathSciNet review:
1249888

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Abstract: A Cauchy integral formula is constructed for solutions to the polynomial Dirac equation , where each is a complex number, is the Dirac operator in , and is defined on a domain in and takes values in a complex Clifford algebra. Some basic properties for the solutions to this equation, arising from the integral formula, are described, including an approximation theorem. We also introduce a Bergman kernel for square integrable solutions to over bounded domains with piecewise , or Lipschitz, boundary.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1249888-8

Article copyright:
© Copyright 1995
American Mathematical Society