L[0,1]^1空间中Volterra积分算子投影方法的研究  

The study of projection method of Volterra integrate operator in L[0,1]^1 space

作　　者：王伟华[1] 傅俊伟[1] 李晓红[1] WANG Weihua;FU Junwei;LI Xiaohong(School of Science,Qiqihar University,Qiqihar 161006,China)

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《高师理科学刊》2020年第11期28-30,共3页Journal of Science of Teachers＇College and University

基　　金：黑龙江省省属高等学校基本科研业务费科研项目(135309478,135109227)。

摘　　要：给出Volterra积分算子在L[0,1]^1空间中利用区间均值代替区间函数值的离散方法,并证明了该方法产生的算子为L[0,1]^1空间中的投影算子,该投影算子具有自伴性且两两不正交性.进而,证明该投影算子点点收敛于单位算子.A numerical discrete method of Velterra integrate opergrate is introduced,the mean of the function on a subinterval is used as a substitute of the original value on the corresponding subinterval in L[0,1]^1 space. It is proved that the operator defined by the method are projection operators defined in L[0,1]^1 space,and the projection operators are self-adjointness and not orthogonal,furthermore that the projection operators pointwisely converge to the identity operators.

关 键 词：均值离散方法 投影算子 Volterra积分算子 

分 类 号：O177.6[理学—数学]