The Hilbert boundary value problem Re{λ(t) p√ψ+(t)} = c(t), t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle |t| = 1,p ≥2 is any definite integer,ψ^+(t)...The Hilbert boundary value problem Re{λ(t) p√ψ+(t)} = c(t), t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle |t| = 1,p ≥2 is any definite integer,ψ^+(t) is the boundary value of the unknown function ψ(z) holomorphic in |z| 〈 1 with single-valued continuous p√ψ+(t) on L.展开更多
Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej+ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f sati...Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej+ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 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 Rn+1 will be investigated.展开更多
文摘The Hilbert boundary value problem Re{λ(t) p√ψ+(t)} = c(t), t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle |t| = 1,p ≥2 is any definite integer,ψ^+(t) is the boundary value of the unknown function ψ(z) holomorphic in |z| 〈 1 with single-valued continuous p√ψ+(t) on L.
基金supported by NNSF of China (11171260)RFDP of Higher Education of China (20100141110054)Scientific Research Fund of Leshan Normal University (Z1265)
文摘Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej+ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 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 Rn+1 will be investigated.