M-matrix asymptotics for Sturm-Liouville problems on graphs

[摘要] We consider a system formulation for Sturm-Liouville operators with formally self-adjoint boundary conditions on a graph. An M-matrix associated with the boundary value problem is defined and related to the matrix Prufer angle associated with the system boundary value problem, and consequently with the boundary value problem on the graph. Asymptotics for the M-matrix are obtained as the eigenparameter tends to negative infinity. We show that the boundary conditions may be recovered, up to a unitary equivalence, from the M-matrix and that the M-matrix is a Herglotz function. This is the first in a series of papers devoted to the reconstruction of the Sturm-Liouville problem on a graph from its M-matrix. (c) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2008-09-01

[效力级别]  Proceedings Paper

[关键词] M-function;sturm-liouville;Prufer angle;differential operators on graphs