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TMF, 2010, Volume 163, Number 1, Pages 17–33 (Mi tmf6484)  

This article is cited in 4 scientific papers (total in 4 papers)

Spectral properties of the generalized Friedrichs model

E. R. Akchurin

Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider the self-adjoint generalized Friedrichs model with small values of the "coupling parameter". In this case, we completely investigate the spectrum of the model and the structure of its eigenvectors (both ordinary and generalized). The constructions we use are based on an analysis of the resolvent of the Friedrichs operator and on the corresponding scattering theory.

Keywords: generalized Friedrichs model, resolvent, spectrum, generalized eigenvector, wave operator

DOI: https://doi.org/10.4213/tmf6484

Full text: PDF file (526 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 163:1, 414–428

Bibliographic databases:

Received: 03.09.2009

Citation: E. R. Akchurin, “Spectral properties of the generalized Friedrichs model”, TMF, 163:1 (2010), 17–33; Theoret. and Math. Phys., 163:1 (2010), 414–428

Citation in format AMSBIB
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\paper Spectral properties of the~generalized Friedrichs model
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. È. R. Akchurin, R. A. Minlos, “Scattering theory for a class of two-particle operators of mathematical physics (the case of weak interaction)”, Izv. Math., 76:6 (2012), 1077–1109  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Lakaev S., Darus M., Kurbanov Sh., “Puiseux Series Expansion for an Eigenvalue of the Generalized Friedrichs Model with Perturbation of Rank 1”, J. Phys. A-Math. Theor., 46:20 (2013), 205304  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Moller J.S., Rasmussen M.G., “The Translation Invariant Massive Nelson Model: II. the Continuous Spectrum Below the Two-Boson Threshold”, Ann. Henri Poincare, 14:4 (2013), 793–852  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. M. É. Muminov, T. Kh. Rasulov, “An eigenvalue multiplicity formula for the Schur complement of a $3\times3$ block operator matrix”, Siberian Math. J., 56:4 (2015), 699–713  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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