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.它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,是Clifford分析中又一类新的函数类,具有一定的研究意义.利用加权双正则函数的Cauchy积分公式与非欧氏距离下的Hile引理,研究了加权双正则函数序列的一些重要性质,例如完备性、等度连续性、列紧性与内闭一致收敛性等.
Regular function is a generalization of analytic function in simple complex analysis in high di mensional space,and weighted regular function is a further development of regular function.It plays an im portant 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 analy sis.Using the Cauchy integral formula of weighted biregular functions and the Hile lemma at non Euclidean distances,this paper researched some important properties of weighted biregular function sequences,such as completeness,equicontinuity,sequential compactness and internally closed uniform convergence etc.
作者
肖卓峰
XIAO Zhuofeng(Institute for Ethnic Groups Attached to Hebei Normal University,Shijiazhuang 050091,China)
出处
《河北师范大学学报(自然科学版)》
2025年第5期450-457,共8页
Journal of Hebei Normal University:Natural Science
基金
国家自然科学基金(12071479)
中央引导地方科技发展资金项目(246Z7608G)。
关键词
加权双正则函数
完备性
等度连续性
列紧性
内闭一致收敛性
weighted biregular functions
completeness
equicontinuity
sequential compactness
inter nally closed uniform convergence
