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Inverse problem for a damped Stieltjes string from parts of spectra
Stockholm University, Faculty of Science, Department of Mathematics. Universit├Ąt Bern, Switzerland.
Number of Authors: 32015 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, no 12, p. 2605-2619Article in journal (Refereed) Published
Abstract [en]

We solve the following inverse problem for boundary value problems generated by the difference equations describing the motion of a Stieltjes string (a thread with beads). Given are certain parts of the spectra of two boundary value problems with two different Robin conditions at the left end and the same damping condition at the right end. From these two partial spectra, the difference of the Robin parameters, the damping constant, and the total length of the string, find the values of the point masses, and of the lengths of the intervals between them. We establish necessary and sufficient conditions for two sets of complex numbers to be the eigenvalues of two such boundary value problems and give a constructive solution of the inverse problem.

Place, publisher, year, edition, pages
2015. Vol. 94, no 12, p. 2605-2619
Keywords [en]
inverse problem, Stieltjes string, Robin boundary condition, damping, continued fraction, Hermite-Biehler polynomial, Prim, 39A60, Sec, 15A29, 30B70, 30H15, 70F17
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-176166DOI: 10.1080/00036811.2014.996874ISI: 000361697900010OAI: oai:DiVA.org:su-176166DiVA, id: diva2:1375844
Available from: 2019-12-06 Created: 2019-12-06 Last updated: 2019-12-06Bibliographically approved

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Pivovarchik, VyacheslavTretter, Christiane
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