A higher order integral representation formula in isotonic Clifford analysis

摘要

Let Δ be the Laplace operator in R~(2n). The aim of this paper is to present an integral representation formula for the solutions of the generalized isotonic system θ_1Δ~kf+iΔ~kfθ_2=0, k ∈ N_0, where θ_1, θ_2 are Dirac type operators and where f stands for the main involution in the complex Clifford algebra C_n. Two special cases of this formula are also discussed, yielding generalizations of the Bochner-Martinelli formula for the holomorphic functions and for the biregular functions.