Some isometrical identities in the wave equation

Abstract

We consider the usual wave equation utt(x,t)=c2uxx(x,t) on the real line with some typical initial and boundary conditions. In each case, we establish a natural isometrical identity and inverse formula between the sourse function and the response function.

Keywords

• wave equation
• isometrical identity
• integral transform
• energy integral
• inverse transform
• Green's function
• Hilbert space.