Sturm-Liouville operators with matrix distributional coefficients - Konstantinov, A. Yu.; Konstantinov, O. (Methods of Functional Analysis and Topology, 2017)
The paper deals with the singular Sturm-Liouville expressions l(y) = -(py’)’ + qy with the matrix-valued coefficients p,q such that q=Q’, p^-1, p^-1Q, Qp^-1, Qp^-1Q L_1, where the derivative of the function Q is understood in the sense of distributions. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent convergence is investigated and all self-adjoint, maximal dissipative, and maximal accumulative extensions are described in terms of homogeneous boundary conditions of the canonical form.