Geodesic
Method of similar operators in research of spectral properties of difference operators with growthing potential
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 673-689

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We study a difference operator with a general growing potential. We obtain asymptotic formulas for the eigenvalues, eigenvectors, and the spectral projections of such operators. We also obtain estimates for the equiconvergence of spectral decompositions. For an invertible difference operator, we estimate off-diagonal decay of the matrix of the inverse operator and the Fourier coefficients of the eigenvectors.
Keywords: difference operator, similar operator method, eigenvalue, eigenvector, spectral projector. 
@article{SEMR_2017_14_a118,
     author = {G. V. Garkavenko and N. B. Uskova},
     title = {Method of similar operators in research of spectral properties of difference operators with growthing potential},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {673--689},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a118/}
}
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G. V. Garkavenko; N. B. Uskova. Method of similar operators in research of spectral properties of difference operators with growthing potential. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 673-689. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a118/