Article
Ufa Mathematical Journal
Volume 8, Number 3, pp. 22-40
Properties of the resolvent of the Laplace operator on a two-dimensional sphere and a trace formula
Atnagulov A.I., Fazullin Z.Yu., Sadovnichii V.A.
DOI:10.13108/2016-8-3-22
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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 $W^1_2(S^2)$.