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

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.