摘要
正则函数是单复分析中解析函数在高维空间的推广,加权正则函数是正则函数的进一步发展.加权正则函数在解决各项异性介质的热传导问题上发挥着重要作用.加权双正则函数又是加权正则函数的进一步发展,加权双正则函数是Clifford分析中的又一类新的函数类,具有一定的研究意义.作者首先证明了加权双正则函数的Cauchy-Pompeiu公式,进而得到了加权双正则函数的Cauchy积分公式,最后证明了加权双正则函数的Cauchy型积分算子的边界性质.
Regular function is a generalization of analytic function in simple complex analysis in high dimensional space,and weighted regular function is a further development of regular function.Weighted regular function plays an important role in solving the heat conduction problem of anisotropic media.Weighted biregular function is a further development of weighted regular function,which is another new class of functions in Clifford analysis.This paper first proves the Cauchy-Pompeiu formula of weighted biregular function,then obtains the Cauchy integral formula of weighted biregular function,and finally proves the boundary properties of Cauchy type integral operator of weighted biregular function.
作者
王龙优
肖卓峰
王丽萍
WANG Longyou;XIAO Zhuofeng;WANG Liping(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Minzu College,Hebei Normal University,Shijiazhuang 050091,China)
出处
《数学年刊(A辑)》
2025年第3期333-350,共18页
Chinese Annals of Mathematics
基金
中央引导地方科技发展资金项目(No.246Z7608G)
国家自然科学基金(No.12071479No.11401162)的资助。
