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
B. P. Allahverdiev. "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.
VANCOUVER
Allahverdiev, B. P. Dilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems. Bulletin of the Iranian Mathematical Society, 2014; 40(6): 1553-1571.