Terumi Touhei

On the Spectral Representation of Green's function for a Layered Acoustic Medium by Means of the Concept of the Hyperfunction

The purpose of this research is to derive the spectral representation of Greens function for an acoustic layered medium by means of the concept of the Hyperfunction . The concept of the Hyperfunction used here is that the Hyperfunction is the result of the difference of the boundary values of the wave function on the spectrum in the complex wavenumber plane . The eigenfunction for the continuous spectrum is assumed to be the Hyperfunction due to Greens functi oni n the resolvent set. Greens function in the resolvent set satisfies the radiation condition , so that the definition and calculation for the energy integral for the continuous spectrum is carried out without any difficulty. As a result, the kernel of the integral for the continuous spectrum is decomposed into eigenfunctions. The decompoesd form agrees with the previous result which the author showed.