微分、差分域中的Wronskian行列式  

WRONSKIAN DETERMINANTS OVER DIFFERENTIAL AND DIFFERENCE FIELDS

作　　者：李应弘[1] 冯如勇[1] 

机构地区：[1]中国科学院数学机械化重点实验室,北京100190

出　　处：《系统科学与数学》2011年第5期620-628,共9页Journal of Systems Science and Mathematical Sciences

基　　金：受国家自然科学基金委青年基金(10901156);创新群体(NSFC60821002/F02)资助课题

摘　　要：众所周知,给定微分或差分域上一组元素,它们在常数域上线性相关当且仅当它们所对应的Wronskian行列式或者Casoratian行列式为零.文章将这个结果推广到具有微分导子和差分导子的微分差分域;同时基于Okugawa的工作,还将结果推广到特征非0的微分差分域.It is well-known that given finitely many of elements in a differential filed （difference field）,these elements are linearly dependent over its constant field if and only if the corresponding Wronskian determinant（Casoratian determinant）vanishes.This paper generalizes these classical results into differential-difference fields,that is,the field including both differential operators and shift operators.Based on Okugawa＇s work,the results are generalized to differential-difference fields with positive characteristic.

关 键 词：微分差分域 WRONSKIAN行列式 微分导子 差分导子 迭代微分导子 

分 类 号：O151.22[理学—数学]