The hilbert boundary value problem for generalized analytic functions in clifford analysis

Let ?_0,n be the real Clifford algebra generated by e₁, e₂,…, e_n satisfying e_ie_j+e_je_i=−2δ_ij, i, j=1,2,…, n. e₀ is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation

equation(0.1)

Lf=0,$Lf=0,$

where

L=q₀e₀∂x₀+ q₁e₁∂x₁+…+qnen_∂xn,$L=q_0{e}_0\partial x_0+\hspace{0.17em}{q}_1{e}_1\partial x_1+\dots +q_n{e}_n{\partial }_{x_n},$

qi <0, i=0,1,…, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in ?ⁿ⁺¹₊ will be investigated.