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Separation of the Sturm–Liouville differential operator with an operator potential
Applied Mathematics and Computation, 2004The vector-valued Sturm-Liouville differential operator \[ Ay(x)=-\frac{d}{dx}(\mu(x)\frac{dy}{dx})+V(x)y(x), \] is considered, where \(V(x)=(v_{ij}(x))_{i,j=1}^\infty \) is a bounded operator and \(\mu(x)\) is a positive \(C^1\)-function in \(\mathbb R\).
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