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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 1, Pages 117-130
doi:10.1155/S0161171284000132

Some isometrical identities in the wave equation

Saburou Saitoh

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

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.