CAJ | 학술논문

讨论了四元数分析中k-左正则函数的若干函数论性质,如cauchy-Pompeiu公式,Cauchy公式,k-左正则函数的表示,Plemelj公式等.同时考虑了k-左正则函数的Riemann边值问题,通过k-左正则函数的Plemelj公式,将问题转化为奇异积分方程组,再利用积分方程理论和压缩映像原理证明了该问题解的存在唯一性.
토론료사원수분석중k-좌정칙함수적약간함수론성질,여cauchy-Pompeiu공식,Cauchy공식,k-좌정칙함수적표시,Plemelj공식등.동시고필료k-좌정칙함수적Riemann변치문제,통과k-좌정칙함수적Plemelj공식,장문제전화위기이적분방정조,재이용적분방정이론화압축영상원리증명료해문제해적존재유일성.
Some function theoretic properties of k-left regular function were considered in Quaternion analysis, such as Cauchy-Pompeiu formula, Cauehy formula, Plemelj formulae and the representation of k-regular function. Applying the theory of integral equations and the contract mapping theorem, the existence and uniqueness of Riemann boundary value problem for k-left regular function was proved.