Premium
Inverse Sturm–Liouville spectral problem on symmetric star‐tree
Author(s) -
Didenko Victor D.,
Rozhenko Natalia A.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2966
Subject(s) - mathematics , sturm–liouville theory , mathematical analysis , equilateral triangle , inverse , dirichlet boundary condition , sequence (biology) , spectrum (functional analysis) , star (game theory) , boundary value problem , inverse problem , dirichlet distribution , square (algebra) , boundary (topology) , function (biology) , pure mathematics , combinatorics , geometry , physics , quantum mechanics , evolutionary biology , biology , genetics
A spectral problem for the Sturm–Liouville equation on the edges of an equilateral regular star‐tree with the Dirichlet boundary conditions at the pendant vertices and Kirchhoff and continuity conditions at the interior vertices is considered. The potential in the Sturm–Liouville equation is a real–valued square summable function, symmetrically distributed with respect to the middle point of any edge. If { λ j }is a sequence of real numbers, necessary and sufficient conditions for { λ j }to be the spectrum of the problem under consideration are established. Copyright © 2013 John Wiley & Sons, Ltd.