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Sturm-Liouville operators with matrix distributional coefficients


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.

Key words: Sturm-Liouville problem, matrix quasi-differential operator, singular coefficients, resolvent approximation, self-adjoint extension.

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TitleSturm-Liouville operators with matrix distributional coefficients
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 1, 51-59
MathSciNet   MR3632388
zbMATH 06810667
Milestones  Received 25/10/2016; Revised 23/11/2016
CopyrightThe Author(s) 2017 (CC BY-SA)

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Alexei Konstantinov
Taras Shevchenko National University of Kyiv, 64 Volodymyrs’ka, Kyiv, 01601, Ukraine

Oleksandr Konstantinov
Livatek Ukraine LLC, 42 Holosiivskyi Ave., Kyiv, 03039, Ukraine

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Alexei Konstantinov and Oleksandr Konstantinov, Sturm-Liouville operators with matrix distributional coefficients, Methods Funct. Anal. Topology 23 (2017), no. 1, 51-59.


@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 = {},


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