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

Fritz Gesztesy·Barry Simon
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Abstract

Let V_0 be a real-valued function on [0,\infty) and V\in L^1([0,R]) for all R>0 so that H(V_0)= -\f{d^2}{dx^2}+V_0 in L^2([0,\infty)) with u(0)=0 boundary conditions has discrete spectrum bounded from below. Let \calM (V_0) be the set of V so that H(V) and H(V_0) have the same spectrum. We prove that \calM(V_0) is connected.

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Fritz Gesztesy, Barry Simon. 2003-07-01. Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schrödinger Operators. https://doi.org/10.1023/b%3Ajoss.0000037217.89500.b3

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