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A description of the location and structure of the essential spectrum of a model operator in a subspace of a Fock space. (English. Russian original) Zbl 1335.35169

Sb. Math. 205, No. 12, 1761-1774 (2014); translation from Mat. Sb. 205, No. 12, 85-98 (2014).
Summary: We consider a certain model operator acting in a subspace of a fermionic Fock space. We obtain an analogue of Faddeev’s equation. We describe the location of the essential spectrum of the operator under consideration and show that the essential spectrum consists of the union of at most four segments.

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81V70 Many-body theory; quantum Hall effect
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