Definition:Convolution Integral/Positive Real Domain

From ProofWiki
Jump to navigation Jump to search

Definition

Let $f$ and $g$ be functions which are integrable.

Let $f$ and $g$ be supported on the positive real numbers $\R_{\ge 0}$ only.

The convolution integral of $f$ and $g$ may be defined as:

$\displaystyle \map f t * \map g t := \int_0^t \map f u \map g {t - u} \rd u$


Also see

  • Results about convolution integrals can be found here.


Sources