A partial inverse problem for the Sturm-Liouville operator on the lasso-graph | Zendy

ChuanFu Yang | Zendy; Natalia P. Bondarenko | Zendy

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A partial inverse problem for the Sturm-Liouville operator on the lasso-graph

Author(s) -

ChuanFu Yang,

Natalia P. Bondarenko

Publication year - 2018

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2019004

Subject(s) - sturm–liouville theory , mathematics , uniqueness , constructive , inverse problem , operator (biology) , graph , a priori and a posteriori , inverse , uniqueness theorem for poisson's equation , boundary value problem , discrete mathematics , mathematical analysis , computer science , biochemistry , chemistry , geometry , repressor , transcription factor , gene , philosophy , process (computing) , epistemology , operating system

The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some additional data. We prove the uniqueness theorem and provide a constructive algorithm for the solution of this partial inverse problem.

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