Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617170 | Journal of Mathematical Analysis and Applications | 2012 | 16 Pages |
Abstract
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 TT and scalar functions m,nm,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 TT. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Konstantin Pankrashkin,