Use Convolve[] function in a proper way?

Questions
1

Hello Group,

I’m having problems getting any return from the Convolve command in MMA 10.3. Here are some examples:

Convolve[E^t, E^-t, t, y]

Convolve[Sin[\[Omega] t], Cos[\[Omega] t], t, y]

Convolve[t, E^t, t, y]

If I do the definition, naturally I get something, for example,

Integrate[E^y E^-(t - y), {y, 0, t}]

GenerateConditions does not help. What bonehead mistake am I making?

thanks,
Whiffee

2

I got same result using M-10.4. Just returns input.

“A bug, not a feature”

3

If you want to match the output of

Integrate[E^y E^-(t - y), {y, 0, t}]

then you need to specify that the functions f and g are only defined for positive arguments, as described here,

Convolve[E^t UnitStep[t], E^-t UnitStep[t], t, y]
4

Jason,

Thanks for the tip. A little experimentation resulted in input that recovered my expected output exactly:

Convolve[ E^y UnitStep[y], E^-y UnitStep[y], y, t, Assumptions -> t > 0]

The same template worked for the other examples I had. Though the form of input looks bizarre, I now feel I can use the command, which makes me feel better.