A mapping method in inverse Sturm-Liouville problems with singular potentials |
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Authors: | A M Savchuk |
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Institution: | (1) Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia |
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Abstract: | In the space L 20, π], the Sturm-Liouville operator L D(y) = ?y″ + q(x)y with the Dirichlet boundary conditions y(0) = y(π) = 0 is analyzed. The potential q is assumed to be singular; namely, q = σ′, where σ ∈ L 20, π], i.e., q ∈ W 2 ?1 0, π]. The inverse problem of reconstructing the function σ from the spectrum of the operator L D is solved in the subspace of odd real functions σ(π/2 ? x) = ?σ(π/2 + x). The existence and uniqueness of a solution to this inverse problem is proved. A method is proposed that allows one to solve this problem numerically. |
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