Geodesic
Spectral properties of the~generalized Friedrichs model
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 17-33

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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. 
@article{TMF_2010_163_1_a1,
     author = {E. R. Akchurin},
     title = {Spectral properties of the~generalized {Friedrichs} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {17--33},
     publisher = {mathdoc},
     volume = {163},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a1/}
}
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E. R. Akchurin. Spectral properties of the~generalized Friedrichs model. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 1, pp. 17-33. http://geodesic.mathdoc.fr/item/TMF_2010_163_1_a1/