Hilbert Space: f(x) = x^n on Interval (0,1)

[Gumbercules]

Homework Statement

for what range of n is the function f(x) = x^n in Hilbert space, on the interval (0,1)? assume n is real.

Homework Equations

functions in Hilbert space are square integrable from -inf to inf

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?

 

[Cyosis]

Yes they are asking you for what n the following integral converges.

<br /> \int_0^1 |f(x)|^2 dx &lt;\infty<br />

 

[Gumbercules]

Thanks!