SPECTRAL PROPERTIES OF CERTAIN DIFFERENTIAL OPERATORS IN UNIFORM WAVEGUIDES

In a domain Ω = ℝ² × (0,1) the equations of linear elasticity are considered. The spatial operators self adjoint extension with respect to Dirichlets boundary condition and its spectral family {P_λ} are studied. The derivative exists almost everywhere and has singularities at discrete lying points λ₁,λ₂,… with λ_j → ∞ as j → ∞. These singularities are connected to resonance effects of the solution to the wave equation of linear elasticity.