两端奇异微分算式乘积自伴域的实参数解描述  

Characterization of Real-parameter Solutions of Self-adjoint Domains for the Products of Differential Expressions Which are Singular at Two Endpoints

作　　者：葛素琴[1] 王万义[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《应用数学》2014年第1期10-17,共8页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11361039)

摘　　要：考虑区间(a,b)上的两端奇异n阶复值系数对称微分算式ly=∑n j=0aj(t)y(j)(t),在其最小算子的实正则型域为Π(T0(l))∩R=(-1,1)及l2 y在L2(a,c]与L2[c,b)中均是部分分离的条件下(c∈(a,b)是任意固定正则点),利用微分方程ly=±λ0y与ly=±μ0y的L2(a,b)解给出微分算式l2 y在区间(a,b)上的自共轭域的完全解析描述,其中λ0,μ0∈Π(T0(l))∩R,λ0,μ0≠0.In this paper,the n-th order symmetric differential expressions with complex value coefficients as following ly=∑i=0nja（t）y^（j）（t）（t∈（a,b））are considered, where botha and b are singular endpoints. Under the assumption that П（T0（l））∩R=（-1,1）, where H（T0 （l）） is the regularity domain of the corresponding minimal operator T0 （l）, and for any a fixed regular point between a and b,l^2 y is partially separated in L^2 （a, c] and L^2 [c, b）, the authors give the complete and analytic characterization for self-adjoint domains of lz y by means of the solutions of equations ly=±λ0y and ly=±μ0y in L^2 （a,b）, where λ0,μ0∈П（T0（l））∩R and λ0,μ0≠0

关 键 词：微分算式的乘积 正则型域 实参数解 部分分离 自共轭域 

分 类 号：O175.3[理学—数学]