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.
Alexei Konstantinov and Oleksandr Konstantinov, Sturm-Liouville operators with matrix distributional coefficients, Methods Funct. Anal. Topology 23
(2017), no. 1, 51-59.
BibTex
@article {MFAT947,
AUTHOR = {Konstantinov, Alexei and Konstantinov, Oleksandr},
TITLE = {Sturm-Liouville operators with matrix distributional coefficients},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {23},
YEAR = {2017},
NUMBER = {1},
PAGES = {51-59},
ISSN = {1029-3531},
MRNUMBER = {MR3632388},
ZBLNUMBER = {06810667},
URL = {http://mfat.imath.kiev.ua/article/?id=947},
}
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