主讲人：加拿大阿尔伯特大学王爱平博士 时间：6月11日下午3:00—4:00 地点：格物楼503 参加人：数学系师生 报告简介： We characterize the self-adjoint domains of general even order linear ordinary differential operators in terms of real-parameter solutions of the differential equation. This is for endpoints which are regular or singular and for arbitrary deficiency index. This characterization is obtained from a new decomposition of the maximal domain in terms of limit-circle solutions. These are the solutions which contribute to the self-adjoint domains in analogy with the celebrated Weyl limit-circle solutions in the second order Sturm-Liouville case. Furthermore, we classify the self-adjoint boundary conditions into three types： separated, coupled and mixed. And we give a construction for all conditions of each type and determine the number of conditions of each type possible for a given self-adjoint domain. Our construction will prove useful in the spectral analysis of these operators and in obtaining canonical forms of self-adjoint boundary conditions. In the case when all d boundary conditions are separated this construction yields explicit non-real conditions for all orders greater than two. It is well known that no such conditions exist in the second order case. |
