Geodesic
Dilation, model, scattering and spectral problems of second-order matrix difference operator
Filomat, Tome 36 (2022) no. 12, p. 3955

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DOI

In the Hilbert space ℓ 2 Ω (Z; E) (Z := {0, ±1, ±2, ...}, dim E = N ∞), the maximal dissipative singular second-order matrix difference operators that the extensions of a minimal symmetric operator with maximal deficiency indices (2N, 2N) (in limit-circle cases at ±∞) are considered. The maximal dissipative operators with general boundary conditions are investigated. For the dissipative operator, a self-adjoint dilation and is its incoming and outgoing spectral representations are constructed. These constructions make it possible to determine the scattering matrix of the dilation. Also a functional model of the dissipative operator is constructed. Then its characteristic function in terms of the scattering matrix of the dilation is set. Finally, a theorem on the completeness of the system of root vectors of the dissipative operator is proved.
DOI : 10.2298/FIL2212955A
Classification : 39A70, 47B39, 47A20, 47A40, 47A45, 47B25, 47B44, 47A75
Keywords: Second-order matrix difference operator, self-adjoint dilation, functional model, scattering matrix, completeness of the system of root vectors 
Bilender P Allahverdiev. Dilation, model, scattering and spectral problems of second-order matrix difference operator. Filomat, Tome 36 (2022) no. 12, p. 3955 . doi: 10.2298/FIL2212955A
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     author = {Bilender P Allahverdiev},
     title = {Dilation, model, scattering and spectral problems of second-order matrix difference operator},
     journal = {Filomat},
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     year = {2022},
     volume = {36},
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     doi = {10.2298/FIL2212955A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2212955A/}
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