- #1

mnb96

- 715

- 5

If

*f*is a morphism between two vector spaces, we say it is linear if we have:

1) [itex]f(x+y) = f(x) + f(y)[/itex]

2) [itex]f(ax) = af(x)[/itex]

Now, if

*f*is the

*convolution*operator [itex]\ast[/itex] , we have a binary operation, because convolution is only defined between two functions.

Can we still talk about linearity in this case or it does not make sense?

In case it makes sense, what does the definition of a binary linear operator looks like?