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Damped star graphs of Stieltjes strings


Authors: M. Möller and V. Pivovarchik
Journal: Proc. Amer. Math. Soc. 145 (2017), 1717-1728
MSC (2010): Primary 47B39; Secondary 34A55, 39A70
DOI: https://doi.org/10.1090/proc/13367
Published electronically: October 20, 2016
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Abstract: We consider a direct and an inverse problem arising in the theory of small transverse vibrations of a star graph of Stieltjes strings damped at the midpoint. The exterior vertices of the graph are supposed to be fixed. We give necessary and sufficient conditions on a sequence of complex numbers to be the spectrum of such a problem.


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Additional Information

M. Möller
Affiliation: The John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, WITS 2050, Johannesburg, South Africa
Email: manfred.moller@wits.ac.za

V. Pivovarchik
Affiliation: Department of Higher Mathematics and Statistics, South Ukrainian National Pedagogical University, 26, Staroportofrankovskaya str., Odessa, 65020, Ukraine
Email: vpivovarchik@gmail.com

DOI: https://doi.org/10.1090/proc/13367
Keywords: Star graph, inverse problem, transverse vibrations, damped vibration, Dirichlet boundary condition, Neumann boundary condition, Hermite-Biehler polynomial, Nevanlinna function
Received by editor(s): December 19, 2015
Received by editor(s) in revised form: June 19, 2016
Published electronically: October 20, 2016
Communicated by: Michael Hitrik
Article copyright: © Copyright 2016 American Mathematical Society