dc.contributor.author Ashrafyan, Yuri dc.contributor.author Michels, Dominik L. dc.date.accessioned 2020-09-14T11:52:56Z dc.date.available 2020-09-14T11:52:56Z dc.date.issued 2020-08-29 dc.identifier.uri http://hdl.handle.net/10754/665126 dc.description.abstract We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is shown that there is a curve in the boundary parameters' domain on which no analog of it is possible. Necessary conditions of the $n$-th eigenvalue are identified, which allows to state the theorems. In addition, several properties of the first eigenvalue are examined. Lower and upper bounds are identified, and the areas are described in the boundary parameters' domain on which the sign of the first eigenvalue remains unchanged. This paper contributes to inverse spectral theory as well as to direct spectral theory. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/2008.13035 dc.rights Archived with thanks to arXiv dc.title On Ambarzumyan-type Inverse Problems of Vibrating String Equations dc.type Preprint dc.contributor.department Visual Computing Center (VCC) dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.contributor.department Computer Science Program dc.eprint.version Pre-print dc.identifier.arxivid 2008.13035 kaust.person Ashrafyan, Yuri kaust.person Michels, Dominik L. refterms.dateFOA 2020-09-14T11:53:29Z
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