Clifford分析中双正则函数的Laurent展式和Liouville定理  

Laurent expansion and Liouville theorem of biregular function in Clifford analysis

作　　者：王海燕[1] 刘杰[2] 彭维玲[3,4] 谢永红[4] 乔玉英[4] 

机构地区：[1]石家庄外经贸职业学院基础部,河北石家庄050061 [2]石家庄铁道学院土木工程分院,河北石家庄050043 [3]吉林通化师范学院数学学院,吉林通化134002 [4]河北师范大学数学与信息科学学院,河北石家庄050016

出　　处：《高校应用数学学报（A辑）》2009年第3期324-334,共11页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10771049);河北省自然科学基金(A2007000225)

摘　　要：利用特异边界的Cauchy积分公式,得到了双正则函数的Laurent展式,留数定理;Cauchy核展开,给出了双正则函数一种新的展式,得到了展式中各项的Cauchy估计,而后定义了可去奇点,通过其充要条件得到了Liouville定理.In this paper, firstly, the Laurent expansion for biregular function is obtained resorting to the Cauchy integral formula on certain distinguished boundary. After that, residue theorem is given. Secondly, a new expansion of biregular function is introduced by developing Cauchy kernel. Cauchy estimate for each part of expansion is discussed. Therefore, Liouville theorem is studied on the basis of removable singular point and its sufficient and necessary condition.

关 键 词：双正则函数 Laurent展式 留数定理 Cauchy估计 LIOUVILLE定理 

分 类 号：O177.4[理学—数学]