Ambarzumian's theorem for trees
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The classical Ambarzumian's Theorem for Schrödinger operators -D2 + q on an interval, with Neumann conditions at the endpoints, says that if the spectrum of (-D2 + q) is the same as the spectrum of (-D2) then q = 0. This theorem is generalized to Schrödinger operators on metric trees with Neumann conditions at the boundary vertices.
CitationCarlson, R., & Pivovarchik, V. (2007). Ambarzumian's theorem for trees. Electronic Journal of Differential Equations, 2007(142), pp. 1-9.
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