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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Pankrashkin, Konstantin

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

DOI  :  10.1016/j.jmaa.2012.07.005

来源: Elsevier

【 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.

【 授权许可】

Free