Some applications of integrated integral operators and Cauchy–Pompeiu representations in Clifford analysis†

†Dedicated to Professor H. Begehr on his 65th Birthday.

Abstract

By using the higher-order Cauchy–Pompeiu formula for functions taking values in a Clifford algebra, the class of generalized regular functions is defined. Some properties, such as the Cauchy integral representation, the Cauchy theorem, Momera's theorem, total analyticity and extension theorem of Hartog's type from theory of regular functions in Clifford analysis, are generalized for those functions.

†Dedicated to Professor H. Begehr on his 65th Birthday.

Keywords:

• Cauchy–Pompeiu representation
• Regular functions
• Bianalytic functions
• Total analyticity
• Multi-biregular functions

AMS Subject Classifications::

• 35C15
• 30620
• 30635
• 44A15
• 46E20

Notes

†Dedicated to Professor H. Begehr on his 65th Birthday.