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

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.