On the number of eigenvalues of the family of operator matrices

• Main Authors: Muminov, Mukhiddin, Rasulov, T. H.
• Format: Article
• Published: St. Petersburg National Research University of Information Technologies, Mechanics and Optics 2014
• Subjects: QA Mathematics
• Online Access: http://eprints.utm.my/id/eprint/59855/; http://nanojournal.ifmo.ru/en/wp-content/uploads/2014/10/NPCM55P619.pdf
• Institution: Universiti Teknologi Malaysia

We consider the family of operator matrices H(K), K ∈ T3 := (−π; π]3 acting in the direct sum of zero-, one- and two-particle subspaces of the bosonic Fock space. We find a finite set Λ ⊂ T3 to establish the existence of infinitely many eigenvalues of H(K) for all K ∈ Λ when the associated Friedrich...