Abstract
The kernel of the branch line integral of Green's function for elastic layered media is decomposed into eigenfunctions for the continuous spectrum via the concept of the Hyperfunction. The kernel of the branch line integral is due to the differences of the boundary values of Green's function in the wavenumber domain on the continuous spectrum. Therefore, the kernel of the branch line integral can be regarded to be the Hyperfunction whose definition function is Green's function in the resolvent set that is in the complex wavenumber plane. Green's function in the resolvent set satsifies the radiation condition, so that the definition and the calculation of the energy integral for the continuous spectrum can be carried out naturally. The symmetrical property of the energy integral can also be found in the formulation.
