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TMF, 2010, Volume 164, Number 1, Pages 78–87 (Mi tmf6525)  

This article is cited in 6 scientific papers (total in 6 papers)

The Efimov effect for a model “three-particle” discrete Schrödinger operator

Yu. Kh. Èshkabilov

Ulugbek Uzbekistan National University, Tashkent, Uzbekistan

Abstract: We study the existence of an infinite number of eigenvalues for a model “three-particle” Schrödinger operator $H$. We prove a theorem on the necessary and sufficient conditions for the existence of an infinite number of eigenvalues of the model operator $H$ below the lower boundary of its essential spectrum.

Keywords: essential spectrum, discrete spectrum, Efimov effect

DOI: https://doi.org/10.4213/tmf6525

Full text: PDF file (393 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 164:1, 896–904

Bibliographic databases:

Received: 29.10.2009

Citation: Yu. Kh. Èshkabilov, “The Efimov effect for a model “three-particle” discrete Schrödinger operator”, TMF, 164:1 (2010), 78–87; Theoret. and Math. Phys., 164:1 (2010), 896–904

Citation in format AMSBIB
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\paper The~Efimov effect for a~model ``three-particle'' discrete Schr\"odinger operator
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  • http://mi.mathnet.ru/eng/tmf/v164/i1/p78

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 170:3 (2012), 341–353  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Yu. Kh. Eshkabilov, “On the discrete spectrum of partial integral operators”, Siberian Adv. Math., 23:4 (2013), 227–233  mathnet  crossref  mathscinet  elib
    3. R. R. Kucharov, Yu. Kh. Eshkabilov, “On the number of negative eigenvalues of a partial integral operator”, Siberian Adv. Math., 25:3 (2015), 179–190  mathnet  crossref  mathscinet
    4. G. P. Arzikulov, Yu. Kh. Eshkabilov, “On the essential and the discrete spectra of a Fredholm type partial integral operator”, Siberian Adv. Math., 25:4 (2015), 231–242  mathnet  crossref  mathscinet
    5. T. Kh. Rasulov, Z. D. Rasulova, “Cpektr odnogo trekhchastichnogo modelnogo operatora na reshetke s nelokalnymi potentsialami”, Sib. elektron. matem. izv., 12 (2015), 168–184  mathnet  crossref
    6. Yu. Kh. Èshkabilov, “Spectrum of a model three-particle Schrödinger operator”, Theoret. and Math. Phys., 186:2 (2016), 268–279  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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