Yodgorov, G. R.; Muminov, M. E. Spectrum of a model operator in the perturbation theory of the essential spectrum. (English) Zbl 1178.81074 Theor. Math. Phys. 144, No. 3, 1344-1352 (2005); translation from Teor. Mat. Fiz. 144, No. 3, 544-554 (2005). Summary: We consider a model operator acting in a subspace of a Fock space and obtain a symmetrized analogue of the Faddeev equation. For the operator considered, we describe the position and the structure of its essential spectrum. Cited in 5 Documents MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81Q15 Perturbation theories for operators and differential equations in quantum theory 47A55 Perturbation theory of linear operators Keywords:creation and annihilation operators; essential spectrum; positive operator; compact operator PDFBibTeX XMLCite \textit{G. R. Yodgorov} and \textit{M. E. Muminov}, Theor. Math. Phys. 144, No. 3, 1344--1352 (2005; Zbl 1178.81074); translation from Teor. Mat. Fiz. 144, No. 3, 544--554 (2005) Full Text: DOI References: [1] K. O. Friedrichs, Perturbation of Spectra in Hilbert Space, Amer. Math. Soc., Providence, R. I. (1965). [2] R. A. Minlos and H. Spohn, ”The three-body problem in radioactive decay: The case of one atom and at most two photons,” in: Topics in Statistical and Theoretical Physics (AMS Transl. Ser. 2, Adv. Math. Sci., Vol. 177, R. L. Dobrushin, R. A. Minlos, M. A. Shubin, and A. M. Vershik, eds.), Amer. Math. Soc., Providence, R. I. (1996), pp. 159–193. · Zbl 0881.47049 [3] S. N. Lakaev and T. Kh. Rasulov, Math. Notes, 73, 521–528 (2003). · Zbl 1059.81059 [4] S. N. Lakaev and T. Kh. Rasulov, Funct. Anal. Appl., 37, No.1, 69–71 (2003). · Zbl 1023.81007 [5] D. Mattis, Rev. Modern Phys., 58, 361–379 (1986). [6] V. A. Malyshev and R. A. Minlos, Trudy Sem. Petrovsk., No. 9, 63–80 (1983). [7] S. P. Merkuriev and L. D. Faddeev, Quantum Scattering Theory for Several Particle Systems [in Russian], Nauka, Moscow (1985); English transl.: L. D. Faddeev and S. P. Merkuriev (Math. Phys. Appl. Math., Vol. 11), Kluwer, Dordrecht (1993). · Zbl 0797.47005 [8] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton, N. J. (1967). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.