四元数分析中正则函数与非齐次n阶方程(■~n F)/(■z^n)=f的某些边值问题  

Some Boundary Value Problems for Regular Functions and Inhomogeneous Nth Order Equation(■~n F)/(■z^n)=f in Quaternionic Analysis

作　　者：蒲松[1] 杨丕文[2] 夏嫦[1] 

机构地区：[1]四川师范大学理学院数学系,四川成都610400 [2]四川师范大学数学学院,四川成都610066

出　　处：《数学的实践与认识》2012年第5期155-163,共9页Mathematics in Practice and Theory

摘　　要：主要讨论了四元数空间中正则函数与非齐次n阶方程(■~n F)/(■z^n)=f在超球上的Dirichlet问题和双圆柱上具有任意整数指标的Riemann-Hilbert问题,给出了可解条件和解的积分表示式.Abstract： In this paper,by using methods from analysis ,We investigate the Dirichlet bound-ary value problems on the ball and Riemann-.Hilbert boundary value problems with any inte-ger index on the bicylinder for the regular functions and inhomogeneous nth order equation α^nF/αz^n=f in Quaternionic analysis. The solvable conditions and the integral expressions of the general solution are given.

关 键 词：四元数分析 Dirichlet问题 RIEMANN-HILBERT边值问题 超球 双圆柱 

分 类 号：O175.8[理学—数学]