3
$\begingroup$

Important results in the theory of PDEs regarding boundary-value problems are trace and extension theorems. Since the trace operator essentially acts by restriction to the boundary of the domain, I was wondering how it got the name "trace": who came up with this name, when and why?

$\endgroup$
4
  • 2
    $\begingroup$ The trace operator restricts a function to the boundary of the domain, so one can say that it "traces the boundary of the function". $\endgroup$ Oct 10, 2017 at 14:42
  • $\begingroup$ Tracing being a primitive pre-computer method of image reproduction :-) $\endgroup$
    – J.J. Green
    Oct 10, 2017 at 14:49
  • 2
    $\begingroup$ Not sure the historical order of terminology, but for example in do Carmo's book on curves and surfaces, the trace of a parametrised curve is it's image. One "traces" the curve in space to get the image as one might trace a picture onto a new sheet of paper. Then @CarloBeenakker comment extends that notion to tracing a function along the boundary which is itself the trace in (do Carmo's sense) of the inclusion of the boundary into the domain. $\endgroup$
    – Paul Bryan
    Oct 11, 2017 at 0:06
  • $\begingroup$ Now crossposted to History of Science and Mathematics, see hsm.stackexchange.com/q/6603/4703 $\endgroup$ Oct 17, 2017 at 15:09

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.