TY  - JOUR
ID  - Kurasov2010
LB  - Kurasov2010
AU  - Kurasov, Pavel
AU  - Nowaczyk, Marlena
TI  - Geometric properties of quantum graphs and vertex scattering matrices
ST  - Geometric properties of quantum graphs and vertex scattering matrices
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 3
SP  - 295
EP  - 309
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.3.295
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.3.295
AB  - Differential operators on metric graphs are investigated. It is proven that vertex matching (boundary) conditions can be successfully parameterized by the vertex scattering matrix. Two new families of matching conditions are investigated: hyperplanar Neumann and hyperplanar Dirichlet conditions. Using trace formula it is shown that the spectrum of the Laplace operator determines certain geometric properties of the underlying graph.
KW  - scattering theory
KW  - quantum graphs
KW  - matching (boundary) conditions
SN  - 1232-9274
ER  -