On the scattering problem and problem of recovery of the shape of a graph
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...
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| Date: | 2024 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8151 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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| DOI: | 10.3842/umzh.v76i8.8151 |