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A Gelfand-Levitan trace formula for generic quantum graphs

Published 23 Jan 2019 in math-ph, math.MP, math.SP, and quant-ph | (1901.07790v2)

Abstract: We formulate and prove a Gelfand-Levitan trace formula for general quantum graphs with arbitrary edge lengths and coupling conditions which cover all self-adjoint operators on quantum graphs, except for a set of measure zero. The formula is reminiscent of the original Gelfand-Levitan result on the segment with Neumann boundary conditions.

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