Definition:Convolution Integral/Positive Real Domain
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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:
- $\ds \map f t * \map g t := \int_0^t \map f u \map g {t - u} \rd u$
Also known as
A convolution integral is also generally known just as a convolution.
However, it has to be borne in mind that the term convolution in general has a wider definition.
Also see
- Results about convolution integrals can be found here.
Sources
- 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $2$: The Inverse Laplace Transform: Solved Problems: The Convolution Theorem: $20$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): convolution
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): convolution