| Autor: |
Mukhiddin I. Muminov, Tulkin H. Rasulov |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
|
| Zdroj: |
Opuscula Mathematica, Vol 35, Iss 3, Pp 371-395 (2015) |
| Druh dokumentu: |
article |
| ISSN: |
1232-9274 |
| DOI: |
10.7494/OpMath.2015.35.3.371 |
| Popis: |
A \(2\times2\) block operator matrix \({\mathbf H}\) acting in the direct sum of one- and two-particle subspaces of a Fock space is considered. The existence of infinitely many negative eigenvalues of \(H_{22}\) (the second diagonal entry of \({\bf H}\)) is proved for the case where both of the associated Friedrichs models have a zero energy resonance. For the number \(N(z)\) of eigenvalues of \(H_{22}\) lying below \(z\lt0\), the following asymptotics is found \[\lim\limits_{z\to -0} N(z) |\log|z||^{-1}=\,{\mathcal U}_0 \quad (0\lt {\mathcal U}_0\lt \infty).\] Under some natural conditions the infiniteness of the number of eigenvalues located respectively inside, in the gap, and below the bottom of the essential spectrum of \({\mathbf H}\) is proved. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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