Convolution of a function with itself

  • Thread starter mhill
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given a function f(t) could we define the operation

[tex] f*f*f*f*f*f*f*f**f*f*f*f*..........*f [/tex] n times ?

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

[tex] (f*f)= \int_{0}^{x}dt f(t)f(t-x) [/tex]

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

mathman

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

[tex] f*f*f*f*f*f*f*f**f*f*f*f*..........*f [/tex] n times ?

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

[tex] (f*f)= \int_{0}^{x}dt f(t)f(t-x) [/tex]

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.
 

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