Convolution of a function with itself

[mhill]

given a function f(t) could we define the operation

$$f*f*f*f*f*f*f*f**f*f*f*f*...*f$$ n times ?

here the operation '*' means convolution of a function if n=2 i know the expression

$$(f*f)= \int_{0}^{x}dt f(t)f(t-x)$$

but i would like to see if this can be applied to arbitrary order , thanks.

 

[mathman]

given a function f(t) could we define the operation

$$f*f*f*f*f*f*f*f**f*f*f*f*...*f$$ n times ?

here the operation '*' means convolution of a function if n=2 i know the expression

$$(f*f)= \int_{0}^{x}dt f(t)f(t-x)$$

but i would like to see if this can be applied to arbitrary order , thanks.

There is nothing in mathematics to prevent you from doing it.