On a family of differential operators with the coupling parameter in the boundary condition
Abstract
We study a family of differential operators L[alpha] in two variables, depending on the coupling parameter [alpha][greaterorequal, slanted]0 that appears only in the boundary conditions. Our main concern is the spectral properties of L[alpha], which turn out to be quite different for [alpha]<1 and for [alpha]>1. In particular, L[alpha] has a unique selfadjoint realization for [alpha]<1 and many such realizations for [alpha]>1. In the more difficult case [alpha]>1 an analysis of nonelliptic pseudodifferential operators in dimension one is involved.
 Publication:

Journal of Computational and Applied Mathematics
 Pub Date:
 November 2007
 Bibcode:
 2007JCoAM.208...57R
 Keywords:

 Irreversible quantum graphs;
 Spectrum