Structures on self-adjoint vertex conditions of local Sturm-Liouville operators on graphs

Boundary value problems

Jia Zhao¹  Guoliang Shi¹ 

[1] Department of Mathematics, Tianjin University, Tianjin, P.R. China

关键词: directed graph;    local operators;    vertex conditions;   

DOI  :  10.1186/s13661-015-0422-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We study the vertex conditions of local Sturm-Liouville operators on metric graphs. Our aim is to give a new description of vertex conditions defining the self-adjoint Sturm-Liouville operators and to clarify the natural geometric structure on the space of complex vertex conditions. Based on this description, we give the self-adjointness results for local Sturm-Liouville operators on finite graphs and the Povzner-Wienholtz-type self-adjointness results for local Sturm-Liouville operators on infinite graphs.

【 授权许可】

CC BY