2022/12/07 by Simonov, Sergey, Woracek, Harald
#34B20 #34B45 #34L40 #47E05 #47J10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2212.03820
We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schrödinger operator on a star-graph with a finite number of finite or infinite edges and an interface condition at the common vertex. A wide class of "selfadjoint" interface conditions, subject to a assumption which is generically satisfied, is considered. We investigate properties of spectral multiplicity of singular spectrum (continuous as well as point) in terms of the spectral data of decoupled operators.