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given two functionsfandgthe operation of convolution [itex]f\ast g[/itex] finds many applications in many different branches of science. However, in such applications, it is typically assumed that one of the two functions (the convolution kernel) is areal scalar field, although the mathematical definition does not impose such constraint.

My question is: does the convolution of, say, two complex-valued functions has any known application? For instance whenf,gare of the kind:

[itex]f:\mathbb{R}^2 \rightarrow \mathbb{C}[/itex], and

[itex]g:\mathbb{R}^2 \rightarrow \mathbb{C}[/itex] ?

Note that such functions could represent, for instance, vector fields on the Cartesian plane.

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# Question on convolution

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