一类具有内部奇异点的微分算式乘积的自伴域  

Characterization of Self-adjoint Domains for the Product of Differential Expressions with an Interval Singular Point

作　　者：葛素琴[1] 王万义[2] 

机构地区：[1]内蒙古科技大学数理与生物工程学院,包头014010 [2]包头医学院,包头014040

出　　处：《应用数学学报》2015年第2期244-253,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11361039)资助项目

摘　　要：本文研究一类带有内部奇异点的n阶复值系数对称微分算式ty=Σna_j(t)y^((j))(t)乘积的自共轭域描述问题.通过构造相应的直和空间,应用直和空间的相关理论,在直和空间上生成的相应于l的最小算子T_0(l)的正则型域Π(T_0(l))满足(-r,r)■Π(T_0(l))∩R及l^2在直和空间中是部分分离的条件下,利用微分方程ly=±λy的解给出l^2的自共轭域的完全解析描述,并且确定自共轭边界条件的矩阵仅由微分方程的解在正则点的初始值决定,其中0<r≤1,λ∈(-r,r),λ≠0.In this paper, the characterization of self-adjoint domains for the product of differential expressions which have an interval singular point are investigated, where the differential expressions are n-th order symmetric differential expressions with complex value coefficients as following ly=n∑j=0aj（t）y（j）（t）. For the purpose we constructed a direct sum j=o space, by the theory of direct sum space and under the assumption that the power l2 is partially separated in the direct sum space, and （-r,r）∈∏（T0（l）nRR, where 0 〈 r 〈 1 and ∏（T0 （l）） is the regularity domain of the corresponding minimal operator To （l） generated by 1 on the direct sum space. We give the complete and analytic characterization for self-adjoint domains of the 12 by means of the solutions of equations ly=±λy with ） λ∈（-r,r）,λ≠0. And the matrix defined the boundary conditions is only determined by the initial values of the regular points of the solutions.

关 键 词：微分算式乘积 内部奇异点 正则型域 部分分离 自共轭域 

分 类 号：O175.3[理学—数学]