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An inverse problem for an inhomogeneous string with an interval of zero density
Author(s) -
Mennicken Reinhard,
Pivovarchik Vyacheslav
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310094
Subject(s) - mathematics , string (physics) , zero (linguistics) , interval (graph theory) , sequence (biology) , position (finance) , inverse , spectrum (functional analysis) , mathematical analysis , transverse plane , pure mathematics , combinatorics , mathematical physics , geometry , physics , quantum mechanics , philosophy , linguistics , structural engineering , finance , biology , engineering , economics , genetics
In the present paper we characterize the spectrum of small transverse vibrations of an inhomogeneous string with the left end fixed and the right one moving with damping in the direction orthogonal to the equilibrium position of the string. The density of the string is supposed to be smooth and strictly positive everywhere except of an interval of zero density at the right end. Sufficient (close to the necessary) conditions are given for a sequence of complex numbers to be the spectrum of such a string. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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