O. Konstantinov

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Articles: 1

Sturm-Liouville operators with matrix distributional coefficients

Alexei Konstantinov, Oleksandr Konstantinov

MFAT 23 (2017), no. 1, 51-59

51-59

The paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ with the matrix-valued coefficients $p,q$ such that $$q=Q', \quad p^{-1},\, p^{-1}Q, \,\, Qp^{-1}, \,\, Qp^{-1}Q \in L_1, $$ 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.

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