Spectrum of singular integral operators of theory of elasticity (Q1897932)

The author studies strictly elliptic linear Dirichlet and Neumann boundary value problems for homogeneous anisotropic elastic media. A uniqueness result for solutions is reported. The solution is then represented in the form of a singular integral operator whose properties are considered. In particular it is shown that under certain conditions the eigenvalues are real and with absolute values less than or equal to 1/2. It is also shown that \(-1/2\) is an eigenvalue while 1/2 is not. The discreteness of the spectrum is proved in another publication of the author.