Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Cauchy-Green type formulae in Clifford analysis

Author: John Ryan
Journal: Trans. Amer. Math. Soc. 347 (1995), 1331-1341
MSC: Primary 30G35; Secondary 58G99
MathSciNet review: 1249888
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30G35, 58G99

Retrieve articles in all journals with MSC: 30G35, 58G99

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society