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Title:
M-functions and metric graphs:hierarchy, inverse problems and magnetic fluxes
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Abstract:
Schrödinger operators on metric graphs, also known as quantum graphs, are determined by the underlying metric graph, the electric and magnetic potentials and the vertex conditions. If the underlying graph is a tree, then the M-function associated with the degree one vertices determines the operator under certain mild assumptions on the vertex conditions. This talk is devoted to the inverse problem for graphs with cycles. To this end we shall analyse the hierarchy of M-functions appeared when graphs are glued together as well as the dependence of M-functions on the magnetic fluxes through the cycles. Two approaches leading to unique solution of the inverseproblem will be presented:
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