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

作者：Pankrashkin Konstantin^*

来源：Journal of Mathematical Analysis and Applications, 2012, 396(2): 640-655.

DOI：10.1016/j.jmaa.2012.07.005

• Self-adjoint extension
• Weyl function
• Boundary triplet
• Quantum graph
• Metric graph

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.

• 出版日期2012-12-15