Separation of the Sturm--Liouville differential operator with an operator potential
The 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 \(\mathbb R\). The authors present sufficient conditions for \(A\) to be separated in \(H_1(\mathbb R)\) and \(H_2(\mathbb R)\) are satisfied for all \(x\in \mathbb R.\)
scientific article; zbMATH DE number 2118024