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Properties of the resolvent of the Laplace-Beltrami operator on the two-dimensional sphere and a trace formula

“…During the discussion of the results obtained in [1,2] at scientific seminars at the Moscow and Bash kortostan universities, Kh.Kh. Murtazin conjectured that, apparently, the further relaxation of the condi tions on the perturbation v(ω) requires a more detailed knowledge of the properties of the kernel R 0 (ω, ω 0 , z) of the unperturbed resolvent R 0 (z) = (L 0 -z) -1 .…”