Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures

[摘要] We consider a class of self-adjoint extensions using the boundary triplet technique. Assuming that the associated Weyl function has the special form M(z) = (m(z)Id - T)n(z)(-1) with a bounded self-adjoint operator T and scalar functions m, n we show that there exists a class of boundary conditions such that the spectral problem for the associated self-adjoint extensions in gaps of a certain reference operator admits a unitary reduction to the spectral problem for T. As a motivating example we consider differential operators on equilateral metric graphs, and we describe a class of boundary conditions that admit a unitary reduction to generalized discrete Laplacians. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Self-adjoint extension;Weyl function;Boundary triplet;Quantum graph;Metric graph