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The paper is devoted to investigation of the spectrum of a perturbedLaplace-Beltrami operator on manifolds with closed geodesics of the same lengthand where metric is a perturbation of the metric of the unit sphere. As theresult, we give the regularized trace formula for the eigenvalues ??of thisoperator when the metric of manifold is presented in abstract form.

Regularized trace of the Laplace-Beltrami operator perturbed by the function on manifolds with specially perturbed sphere metric