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加拿大阿尔伯特大学王爱平博士讲学通知
澳门新葡新京:系统管理员  发布时间:2012-06-11   浏览次数:20

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

报告概况:

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.

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