THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS

被引：3

作者：

Si, Zhongwei ^{[1
]}

Du, Jinyuan ^{[2
]}

机构：

[1] Leshan Normal Univ, Sch Math & Informat Sci, Leshan 614004, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2013年 / 33卷 / 02期

关键词：

Generalized analytic function; Hilbert boundary value problem; (H)over-cap(mu) function;

D O I：

10.1016/S0252-9602(13)60006-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R-0,R-n be the real Clifford algebra generated by e(1), e(2), ... , e(n) satisfying e(i)e(j) + e(j)e(i) = -2 delta(ij), i, j, = 1, 2, ... ,n. e(0) is the unit element. Let Omega be an open set. A function f is called left generalized analytic in Omega if f satisfies the equation Lf = 0, where L = q(0)e(0)partial derivative(x0) + q(1)e(1)partial derivative(x1) + ... + q(n)e(n)partial derivative(xn), 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 R-+(n+1). will be investigated.

引用

页码：393 / 403

页数：11

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