Some Integral Representation for Meta-Monogenic Function in Clifford Algebras Depending on Parameters

Generalized Cauchy-Riemann-type operators and some integral representation formulas

“…Now we consider the coefficients λ j as matrices with constant entrance. So for λ j , consider the matrix m × m (X j ik ), for i, k = 1,..., m, j = 0,..., n. Then we have the following representation D = ∑ n j=0 (X j ik )e j ∂ j for the operator given by (1). In the case that X j ik = X j ki , the operator D becomes a symmetric matrix operator.…”

“…Example 1. The operator D defined by (1) and with coefficients in A 1 leads in A 1 to the first order system Du = (λ 0 ∂ 0 + λ 1 e 1 ∂ 1 )(u 0 + u 1 e 1 ) = 0, where λ 0 = λ 00 + λ 01 e 1 and λ 1 = λ 10 + λ 11 e 1 . Example 2.…”

“…Under certain conditions the study of the boundary value problems can be reduced to a fixed-point problem for an operator defined through a fundamental solution [1,5]. In this section we present some integral formulas that can be also used to solve boundary value problems.…”

About the Dirichlet Boundary Value Problem using Clifford Algebras

“…• The relations in (4) are called structure relations of the Clifford Algebra. See [28,29] • A n is a linear space of dimension Recently, Clifford analysis associated to new algebraic structures has attracted special attention.…”