Про задачу розсіяння та задачу відновлення форми графа

O. Boyko; O. Martynyuk; V. Pivovarchik

doi:10.3842/umzh.v76i8.8151

O. Boyko Southern Ukrainian National Pedagogical University named after K. D. Ushinsky, Odesa
O. Martynyuk Southern Ukrainian National Pedagogical University named after K. D. Ushinsky, Odesa
V. Pivovarchik Southern Ukrainian National Pedagogical University named after K. D. Ushinsky, Odesa; University of Vaasa, Finland

DOI: https://doi.org/10.3842/umzh.v76i8.8151

Keywords: Sturm-Liouville equation, eigenvalue, equilateral tree, star graph, Dirichlet boundary condition, Neumann boundary condition, lead, S-function, asymptotics.

Abstract

UDC 517.9

We consider a scattering problem generated by the Sturm–Liouville equation on a tree formed by an equilateral compact subtree with a lead (a half-infinite edge) attached to this compact subtree. It is assumed that the potential on the lead by is identically equal to zero and the potentials on finite edges are real $L_2$-functions. We show how to determine the shape of the tree by using the S-function and the eigenvalues of the scattering problem.

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On the scattering problem and problem of recovery of the shape of a graph

Abstract

References