Geodesic
The matrix analysis of spectral projections for the perturbed self-adjoint operators
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 369-405

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We study bounded perturbations of an unbounded positive definite self-adjoint operator with discrete spectrum. The spectrum has semi-simple eigenvalues with finite geometric multiplicity and the perturbation belongs to operator space defined by rate of the off-diagonal decay of the operator matrix. We show that the spectral projections and the resolvent of the perturbed operator belong to the same space as the perturbation. These results are applied to the Hill operator and the operator with matrix potential. We also consider the inverse problem and the modified Galerkin method.
Keywords: the method of similar operators, the Hill operator, spectral projection. 
@article{SEMR_2019_16_a130,
     author = {N. B. Uskova},
     title = {The matrix analysis of spectral projections for the perturbed self-adjoint operators},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {369--405},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a130/}
}
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N. B. Uskova. The matrix analysis of spectral projections for the perturbed self-adjoint operators. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 369-405. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a130/