Eigenvalues of infinite non-compact star graph
G. Mutlu
We consider the Schrödinger operator on an infinite non-compact star graph which has countably infinite number of semi-infinite rays emanating from the single vertex of the graph.
We impose the most general vertex conditions at the central vertex. We transfer this boundary value problem on the infinite non-compact quantum star graph to Schrödinger equation
on the half-line with operator coefficients in an infinite dimensional separable Hilbert space.
We obtain the characteristic function of this boundary value problem which is the Jost function of the Schrödinger equation on the half-line with operator coefficients.
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