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

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