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# The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles

### Abstract

A model operator associated with the energy operator of a system of three non conserved number of particles is considered. The essential spectrum of the operator is described by the spectrum of a family of the generalized Friedrichs model. It is shown that there are infinitely many eigenvalues lying below the bottom of the essential spectrum, if a generalized Friedrichs model has a zero energy resonance.

Key words: Operator energy, non conserved number of particles, eigenvalues, Efimov effect, Faddeev-Newton equations, essential spectrum, Hilbert-Schmidt operators, infinitely many eigenvalues.

### Article Information

 Title The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 1-16 MathSciNet MR2308575 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

Sergio Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr. 6, D-53115, Bonn, Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; IZKS; CERFIM, Locarno, Switzerland; Accademia di Architettura, Mendrisio, Switzerland

Saidakhmat N. Lakaev
Samarkand State University, 15 University Boulevard, Samarkand, 703004, Uzbekistan

Tulkin H. Rasulov
Samarkand State University, 15 University Boulevard, Samarkand, 703004, Uzbekistan

### Citation Example

Sergio Albeverio, Saidakhmat N. Lakaev, and Tulkin H. Rasulov, The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles, Methods Funct. Anal. Topology 13 (2007), no. 1, 1-16.

### BibTex

@article {MFAT368,
AUTHOR = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Rasulov, Tulkin H.},
TITLE = {The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {1},
PAGES = {1-16},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=368},
}