International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 117-130

Some isometrical identities in the wave equation

Saburou Saitoh

Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu 376, Japan

Received 30 April 1983

Copyright © 1984 Saburou Saitoh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.