Pavel Exner and Ondrej Turek
Approximations of singular vertex couplings in quantum graphs
(2714K, Postscript)

ABSTRACT.  We discuss approximations of the vertex coupling on a star-shaped 
quantum graph of $n$ edges in the singular case when the wave 
functions are not continuous at the vertex and no edge-permutation 
symmetry is present. It is shown that the Cheon-Shigehara 
technique using $\delta$ interactions with nonlinearly scaled 
couplings yields a $2n$-parameter family of boundary conditions in 
the sense of norm resolvent topology. Moreover, using graphs with 
additional edges one can approximate the ${n+1\choose 
2}$-parameter family of all time-reversal invariant couplings.