| Title:
|
Extensions, dilations and functional models of infinite Jacobi matrix (English) |
| Author:
|
Allahverdiev, B. P. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
593-609 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space of boundary values is constructed for the minimal symmetric operator generated by an infinite Jacobi matrix in the limit-circle case. A description of all maximal dissipative, accretive and selfadjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a selfadjoint dilation of maximal dissipative operator and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We construct a functional model of the dissipative operator and define its characteristic function. We prove a theorem on the completeness of the system of eigenvectors and associated vectors of dissipative operators. (English) |
| Keyword:
|
infinite Jacobi matrix |
| Keyword:
|
symmetric operator |
| Keyword:
|
selfadjoint and nonselfadjoint extensions |
| Keyword:
|
maximal dissipative operator |
| Keyword:
|
selfadjoint dilation |
| Keyword:
|
scattering matrix |
| Keyword:
|
functional model |
| Keyword:
|
characteristic function |
| Keyword:
|
completeness of the system of eigenvectors and associated vectors |
| MSC:
|
47A20 |
| MSC:
|
47A40 |
| MSC:
|
47A45 |
| MSC:
|
47B25 |
| MSC:
|
47B36 |
| MSC:
|
47B39 |
| MSC:
|
47B44 |
| idZBL:
|
Zbl 1081.47036 |
| idMR:
|
MR2153085 |
| . |
| Date available:
|
2009-09-24T11:25:51Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128005 |
| . |
| Reference:
|
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