What is the definition of the p successive convolutions of an impulse response g(n)? (p is an integer)?

Question

I'm reading chapter 13 of the book Neural Networks - A comprehensive foundation by Simon Haykin. The book described the tap delay line memory. g(n) is the impulse response of the memory.

Answer 1

A tap delay line is simply a bunch of memory storage devices that will delay the data (or signal).

p successive convolutions of g(n) is the same as the Fourier transform of g(n) to the p-th power. I don't recall but it seems like that might be a propertry of convolution/Fourier transform.