Geodesic
Spectrum and resolvent of a block operator matrix
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 334-344

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In the paper the block operator matrix $H$ associated with the system of at most three quantum particles on a $\mathrm{d}$-dimensional lattice is considered. Spectrum of this operator is studied in detail. In particular, it is shown that the operator $H$ has at most four simple eigenvalues lying outside of the essential spectrum. Moreover, the resolvent of $H$ is founded.
Keywords: Block operator matrix, Fock space, annihilation and creation operators, generalized Friedrichs model, Fredholm's determinant, essential and discrete spectrum, resolvent. 
@article{SEMR_2014_11_a77,
     author = {T. H. Rasulov and I. O. Umarova},
     title = {Spectrum and resolvent of a block operator matrix},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {334--344},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a77/}
}
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T. H. Rasulov; I. O. Umarova. Spectrum and resolvent of a block operator matrix. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 334-344. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a77/