# Hilbert space basics

1. Jul 31, 2009

### Gumbercules

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?

2. Jul 31, 2009

### Cyosis

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

$$\int_0^1 |f(x)|^2 dx <\infty$$

3. Jul 31, 2009

Thanks!