On the eigenvalues of a 2 × 2 block operator matrix
A 2 × 2 block operator matrix 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 H22 (the second diagonal entry of H) is proved for the case where both of the associated Friedrichs models have a zero e...
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AGH University of Science and Technology
2015
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my.utm.586832021-11-03T08:49:19Z http://eprints.utm.my/id/eprint/58683/ On the eigenvalues of a 2 × 2 block operator matrix Muminov, M. I. Rasulov, T. H. Q Science (General) A 2 × 2 block operator matrix 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 H22 (the second diagonal entry of 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 H22 lying below z < 0; the following asymptotics is found (Formula presented.) 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 H is proved. AGH University of Science and Technology 2015 Article PeerReviewed Muminov, M. I. and Rasulov, T. H. (2015) On the eigenvalues of a 2 × 2 block operator matrix. Opuscula Mathematica, 35 (3). pp. 371-395. ISSN 1232-9274 http://dx.doi.org/10.7494/OpMath.2015.35.3.371 DOI: 10.7494/OpMath.2015.35.3.371 |
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Q Science (General) Muminov, M. I. Rasulov, T. H. On the eigenvalues of a 2 × 2 block operator matrix |
| description |
A 2 × 2 block operator matrix 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 H22 (the second diagonal entry of 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 H22 lying below z < 0; the following asymptotics is found (Formula presented.) 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 H is proved. |
| format |
Article |
| author |
Muminov, M. I. Rasulov, T. H. |
| author_facet |
Muminov, M. I. Rasulov, T. H. |
| author_sort |
Muminov, M. I. |
| title |
On the eigenvalues of a 2 × 2 block operator matrix |
| title_short |
On the eigenvalues of a 2 × 2 block operator matrix |
| title_full |
On the eigenvalues of a 2 × 2 block operator matrix |
| title_fullStr |
On the eigenvalues of a 2 × 2 block operator matrix |
| title_full_unstemmed |
On the eigenvalues of a 2 × 2 block operator matrix |
| title_sort |
on the eigenvalues of a 2 × 2 block operator matrix |
| publisher |
AGH University of Science and Technology |
| publishDate |
2015 |
| url |
http://eprints.utm.my/id/eprint/58683/ http://dx.doi.org/10.7494/OpMath.2015.35.3.371 |
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1717093383051149312 |