摘要
该文主要讨论了由正则和奇异的4阶对称微分算式生成的微分算子的积算子的自伴性,得到了I(I=[a,b]或[a,+∞))上的积算子L=L2L1是自伴算子,当且仅当AQ_4^(-1)(0)C=BQ_4^(-1)(0)D;I上的幂算子L_1^(2)是自伴的充要条件是L1是自伴的,并且给出了反例,说明2个自伴算子的积不一定是自伴算子,不同的非自伴算子的积可以是自伴算子。
The adjointness of the product of two differential operators generated by a fourth order symmetric differential expression is discussed. When both I=[ a , b ] and I = [ a , +∞) , it is proved if L1 and L2 are self-adjoint differential operators, then L = L2 L1 is self-adjoint if and only if L1 = L2 and L2 is self-adjoint if and only if L1 = L2 . Two examples are given. Examples prove that the product of two self-adjoint operators may not be a self-adjoint operators and the product of two different non-self-adjoint operators may be self-adjoint operators.
出处
《南京理工大学学报》
EI
CAS
CSCD
北大核心
2003年第6期738-742,共5页
Journal of Nanjing University of Science and Technology
关键词
对称微分算式
微分算子
自伴算子
symmetric differential expression, differential operator, self-adjoint operator
