Homogeneity of a String having Three Unperturbed Spectra
Vyacheslav Pivovarchik · Birkhäuser Basel eBooks · 2000
We prove that there does not exist a smooth inhomogeneous string such the spectra of three particular boundary value problems describing its small vibrations coincide with those for a homogeneous string. These three boundary value problems are the Dirichlet problem on [0, 1 / 2 ],the Dirichlet problem on [ 1 / 2 , l ] ,and the Dirichlet-Neumann problem on[0, l ].