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Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators


Let V 0be a real-valued function on [0,∞) and VL 1([0,R]) for all R>0 so that H(V 0)=−\(\frac{{d^2 }}{{dx^2 }}\)+V 0in L 2([0,∞)) with u(0)=0 boundary conditions has discrete spectrum bounded from below. Let \(M\)(V 0) be the set of Vso that H(V) and H(V 0) have the same spectrum. We prove that \(M\)(V 0) is connected.

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Gesztesy, F., Simon, B. Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators. Journal of Statistical Physics 116, 361–365 (2004).

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  • isospectral sets of potentials
  • half-line Schrödinger operators
  • inverse problems