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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cauchy-Green type formulae in Clifford analysis
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by John Ryan PDF
Trans. Amer. Math. Soc. 347 (1995), 1331-1341 Request permission

Abstract:

A Cauchy integral formula is constructed for solutions to the polynomial Dirac equation $({D^k} + \sum \nolimits _{m = 0}^{k - 1} {{b_m}{D^m})f = 0}$, where each ${b_m}$ is a complex number, $D$ is the Dirac operator in ${R^n}$, and $f$ is defined on a domain in $^{{R^n}}$ 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 $(D + \lambda )f = 0$ over bounded domains with piecewise ${C^1}$, or Lipschitz, boundary.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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