Function-type arguments in function definition

*To*: mathgroup at smc.vnet.net*Subject*: [mg44267] Function-type arguments in function definition*From*: "Carsten Reckord" <news at reckord.de>*Date*: Tue, 4 Nov 2003 03:23:37 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I'm pretty new to Mathematica so please excuse me if this is kind of a silly question (though I couldn't find any answer after a full day of searching). I'm trying to define functions that take other functions as arguments and need those functions' arguments in their own definition. An example would be the definition of convolution: h(x)=f(x)*g(x) is defined as Integral over f(y)g(x-y) with respect to y. As you can see it is important in the definition of convolution to treat the arguments f and g as functions because the definition makes use of their arguments. I've seen this done in Mathematica as convolute[f_,g_,x_]:=Integrate[f[y]*g[x-y],{y,-inf,inf}] but that's not exactly what I'm looking for because I can only use function names as arguments to convolute[...], not arbitrary expressions in x. So I can't for example use it for the convolution f(s(x))*g(t(x)) without defining intermediate functions for f(s(x)) and g(t(x))... So, my question is if there is any way to define such a function that can make use of its arguments being functions and yet supports arbitrary expressions as its arguments? Thanks, Carsten