Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters (original) (raw)

Advances in Applied Clifford Algebras, 2013

Abstract

In recent years, the integral representation problems have been studied in many context and generalities. For example, for the monogenic and meta functions in some Clifford type algebras, see [10, 11].In this paper we construct a Cauchy-Pompeiu type formula for meta-monogenic operator of order {n, (D-\lambda)^n, \lambda \in \mathbb{R}}$$n,(D-λ)n,λ∈R, and its conjugate {(\overline{D} - \lambda)^n}$$(D¯-λ)n in a Clifford algebra depending on parameters {\mathcal{A}_n(2, \alpha_j, \gamma_{ij})}$$An(2,αj,γij). Using these explicit representation formula of Cauchy-Pompeiu type we will show some applications.

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