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Hilbert space basics

  1. Jul 31, 2009 #1
    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. jcsd
  3. Jul 31, 2009 #2

    Cyosis

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    Homework Helper

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

    [tex]
    \int_0^1 |f(x)|^2 dx <\infty
    [/tex]
     
  4. Jul 31, 2009 #3
    Thanks!
     
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