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Weinstein Criteria and Regularized Traces in the Case of Transverse Vibrations of an Elastic String with Springs

Weinstein Criteria and Regularized Traces in the Case of Transverse Vibrations of an Elastic... The transverse vibrations of a string with additional restrictions in the form of elastic point constraints are studied. In contrast toWeinstein’s original approach, the constraints are not represented as orthogonality-type conditions in the case under study. Nevertheless, it is shown that the main results of Weinstein’s theory remain valid. It is also shown that the string rigidity coefficients can uniquely be reconstructed from the first-order regularized traces of the corresponding operators. This permits one to give a physical interpretation of regularized traces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Weinstein Criteria and Regularized Traces in the Case of Transverse Vibrations of an Elastic String with Springs

Differential Equations , Volume 54 (1) – Apr 23, 2018

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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266118010020
Publisher site
See Article on Publisher Site

Abstract

The transverse vibrations of a string with additional restrictions in the form of elastic point constraints are studied. In contrast toWeinstein’s original approach, the constraints are not represented as orthogonality-type conditions in the case under study. Nevertheless, it is shown that the main results of Weinstein’s theory remain valid. It is also shown that the string rigidity coefficients can uniquely be reconstructed from the first-order regularized traces of the corresponding operators. This permits one to give a physical interpretation of regularized traces.

Journal

Differential EquationsSpringer Journals

Published: Apr 23, 2018

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