Geodesic
Lagrange formula for differential operators and self-adjoint restrictions of the maximal operator on a tree
Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 16-29

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The paper is devoted to linear differential operators defined on a tree. We aim at obtaining complete descriptions of well-posed restrictions of a given maximal differential operator on a tree. In this paper all self-adjoint restrictions of the maximal operator and also all the invertible restrictions of the maximal operator are described. We also present the Lagrange formula for a differential operator on a tree with the Kirchhoff conditions at its interior vertices. 
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     title = {Lagrange formula for differential operators and self-adjoint restrictions of the maximal operator on a tree},
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B. Kanguzhin; L. Zhapsarbaeva; Zh. Madibaiuly. Lagrange formula for differential operators and self-adjoint restrictions of the maximal operator on a tree. Eurasian mathematical journal, Tome 10 (2019) no. 1, pp. 16-29. http://geodesic.mathdoc.fr/item/EMJ_2019_10_1_a2/