An article by Professor Bilender Allahverdiyev of the Mathematics Department of Khazar University, titled "Non-self-adjoint singular matrix Sturm-Liouville operators with general boundary conditions," has been published in Filomat (2024, Volume 38, No. 30). It should be noted that Filomat journal is indexed in the Web of Science and Scopus databases.
In the Hilbert space the maximal dissipative singular matrix-valued Sturm–Liouville operators that the extensions of a minimal symmetric operator with maximal deficiency indices are studied. The maximal dissipative operators with general boundary conditions are investigated. A self-adjoint dilation is constructed for dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and determine its characteristic function in terms of the scattering matrix of the dilation. Moreover a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative operators proved.
Link to the article: https://www.pmf.ni.ac.rs/filomat-content/2024/38-30/FILOMAT%2038-30.html
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