Hilbert空间L^2[a,b]上m个微分算子积的自伴性  

Self-adjointness of Products of m Differential Operators in the Hilbert Space L^2[a,b]

作　　者：杨传富[1] 黄振友[1] 杨孝平[1] 

机构地区：[1]南京理工大学理学院应用数学系,江苏南京210094

出　　处：《应用数学》2004年第4期617-622,共6页Mathematica Applicata

摘　　要：考虑 [a ,b]( -∞ <a <b<∞ )上n阶复值系数正则对称微分算式ly =∑nj=0 aj(t)y(j) .本文首先给出由lmy(m∈N且m≥ 2 )生成的微分算子T(lm)自伴边条件一种新的描述 ,其次研究了由微分算式ly生成的m个微分算子Tk(l) (k=1 ,… ,m)的积Tm(l)…T2 (l)T1(l)的自伴性并获得其自伴的充分必要条件 .A formally symmetric differential expression of order n,ly=∑n j=0a j(t)y (j) defined on [a,b](-∞<a<b<∞),is considered.We present a new characterization of self-adjoint domains for the differential operators T(lm) generated by lm(m∈N and m≥2).For m differential operators T k(l)(k=1,…,m) associated with l,we study the self-adjointness for product operator T m(l)…T 2(l)T 1(l) and obtain a necessary and sufficient condition for the self-adjointness of T m(l)…T 2(l)T 1(l).

关 键 词：自伴性 微分算子积 边条件 

分 类 号：O175.3[理学—数学]