Geodesic
Properties of the resolvent of the Laplace operator on a~two-dimensional sphere and a~trace formula
Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 22-40

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In the work we study the properties of the resolvent of the Laplace–Beltrami operator on a two-dimensional sphere $S^2$. We obtain the regularized trace formula for the Laplace-Beltrami operator perturbed by the operator of multiplication by a function in $W^1_2(S^2)$.
Keywords: resolvent, Laplace-Beltrami operator, perturbed operator.
Mots-clés : kernel 
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A. I. Atnagulov; V. A. Sadovnichy; Z. Yu. Fazullin. Properties of the resolvent of the Laplace operator on a~two-dimensional sphere and a~trace formula. Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 22-40. http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a3/