Department of Mathematics, Suleyman Demirel University, 32260 Isparta, Turkey
Abstract
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a selfadjoint dilation of the dissipative operator and construct the incoming and outgoing spectral representations that makes it possible to determine the scattering function (matrix) of the dilation. Further a functional model of the dissipative operator and its characteristic function in terms of the Weyl function of a selfadjoint operator are constructed. Finally we show that the system of root vectors of the dissipative operators are complete in the Hilbert space ℓ_{Ω}²(Z;C²).
Allahverdiev, B. P. (2014). Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems. Bulletin of the Iranian Mathematical Society, 40(6), 1553–1571.
MLA
Allahverdiev, B. P. "Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems", Bulletin of the Iranian Mathematical Society, 40, 6, 2014, 1553–1571.
HARVARD
Allahverdiev, B. P. (2014). 'Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems', Bulletin of the Iranian Mathematical Society, 40(6), pp. 1553–1571.
CHICAGO
Allahverdiev, B. P., "Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems." Bulletin of the Iranian Mathematical Society, 40 6 (2014): 1553–1571,
VANCOUVER
Allahverdiev B. P. Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems. BIMS. 2014;40(6):1553–1571.
