1. The problem statement, all variables and given/known data for what range of n is the function f(x) = x^n in Hilbert space, on the interval (0,1)? assume n is real. 2. Relevant equations functions in Hilbert space are square integrable from -inf to inf 3. The attempt at a solution I am having trouble with the language of the problem and the concept of the Hilbert space in general. Does 'on the interval (0,1)' mean that the square integrable function only has to converge for limits of integration between 0 and 1?