| dc.creator |
Allahverdiev, Bilender |
|
| dc.date |
2018-03-29T21:00:00Z |
|
| dc.date.accessioned |
2020-10-06T09:29:49Z |
|
| dc.date.available |
2020-10-06T09:29:49Z |
|
| dc.identifier |
1e570155-f456-462d-b085-0a019f8492b9 |
|
| dc.identifier |
10.1002/mma.4703 |
|
| dc.identifier |
https://avesis.sdu.edu.tr/publication/details/1e570155-f456-462d-b085-0a019f8492b9/oai |
|
| dc.identifier.uri |
http://acikerisim.sdu.edu.tr/xmlui/handle/123456789/54909 |
|
| dc.description |
In this paper, we construct a space of boundary values for minimal symmetric 1D Hamiltonian operator with defect index (1,1) (in limit-point case at a(b) and limit-circle case at b(a)) acting in the Hilbert space L2((a,b);C2). In terms of boundary conditions at a and b, all maximal dissipative, accumulative, and self-adjoint extensions of the symmetric operator are given.Two classes of dissipative operators are studied. They are called dissipative at a and dissipative at b. For 2 cases, a self-adjoint dilation of dissipative operator and its incoming and outgoing spectral representations are constructed. These constructions allow us to establish the scattering matrix of dilation and a functional model of the dissipative operator. Further, we define the characteristic function of the dissipative operators in terms of the Weyl-Titchmarsh function of the corresponding self-adjoint operator. Finally, we prove theorems on completeness of the system ofroot vectors of the dissipative operators. |
|
| dc.language |
eng |
|
| dc.rights |
info:eu-repo/semantics/closedAccess |
|
| dc.title |
Extensions, dilations, and spectral problems of singular Hamiltonian systems |
|
| dc.type |
info:eu-repo/semantics/article |
|