Explicit solution of the inverse problem for a vibrating string

DOI10.1016/0022-247X(83)90227-5zbMath0524.73061MaRDI QIDQ584976

Victor Barcilon

Publication date: 1983

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

reconstruction of density of string from its spectra

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Inverse problems for waves in solid mechanics (74J25) Inverse problems involving ordinary differential equations (34A55) Strings (74K05) Ordinary differential operators (34L99)

Related Items (12)

Geometrical effects in resonant gas oscillations ⋮ Iso-spectral operators: Some model examples with discontinuous coefficients ⋮ Isospectral flows for the inhomogeneous string density problem ⋮ On the uniqueness of the solution of dual equation of a singular Sturm-Liouville problem ⋮ The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points ⋮ Examples and counter-examples for a string density formula in the case of a discontinuity ⋮ A selective review of direct, semi-inverse and inverse eigenvalue problems for structures described by differential equations with variable coefficients ⋮ The uniqueness of the solution of dual equations of an inverse indefinite Sturm--Liouville problem ⋮ A formula for the mass density of a vibrating string in terms of the trace ⋮ Acoustic scattering and the extended Korteweg-de Vries hierarchy ⋮ On the density of the mass distribution of a string at the origin ⋮ On the Reconstruction of a String from Spectral Data

Cites Work

• A generalization of the trace concept
• Extremal solutions of inverse eigenvalue problems with finite spectral data
• A note on a formula of Gelfand and Levitan
• Inverse scattering on the line
• The inverse problem for periodic potentials
• Can One Hear the Shape of a Drum?
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