Standard notation for "open integral"

[qu_bio]

If I have a function defined over an integral, e.g.

$F(t') = \int_{-\infty}^{\infty} dt \tilde{F}(t,t')$

is there a standard way to denote this integral as being "Open", that is to say if I write

$H = F(t') G(t)$

I want this to mean

$H = \int_{-\infty}^{\infty} dt \tilde{F}(t,t') G(t)$

Rather than

$H = [\int_{-\infty}^{\infty} dt \tilde{F}(t,t') ] * G(t)$

I could make up some notation, but I'd rather not if one exists!

Many thanks

 

[certainly]

I don't know too much about this, but I believe a convolution is a closely related concept.

 

[qu_bio]

I don't know too much about this, but I believe a convolution is a closely related concept.

Yes I suppose it looks similar if F(t,t') -> F(t-t'), but my question is a little more general.

 

[certainly]

Yes I suppose it looks similar if F(t,t') -> F(t-t'), but my question is a little more general.

One more difference:-
$\int_{-\infty}^{+\infty}\bar{F}(t'-t)G(t) dt=[\bar{F}\ast G](t')$ not $F(t')$.