A hypercomplex derivative of monogenic functsions in and its Applications

Abstract

We generalize the definition of a certain derivative of regular functions of variables from the four-dimensional real associative algebra of quaternions to monogenic functions of hypercomplex variables in Rⁿ⁺¹. Using this concept of derivation we look for primitives of monogenic functions in the set of monogenic functions. The results will be applied for proving a final result about the invertibility of a hypercomplex II-operator.

Keywords:

• Hypercomplex derivative
• primitives of maonogenic functions
• generalized power series
• singular integral operators

1991 Mathematical Subject Classification:

• 30G35

^∗Corresponding author.

^∗Corresponding author.

Notes

^∗Corresponding author.