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Homework Help: L2 Space check

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data
    Check whether the function [tex]f(x)=x^{-1/3}, 0<x<1,[/tex] belongs to the space
    [tex]L^{2}(0,1)[/tex]


    2. Relevant equations
    Well, I missed this lecture so not really sure how to go about this but from what I gathered:

    A function is in L2 if the function is square integrable

    If that is the case then:


    3. The attempt at a solution

    [tex]\int^{1}_{0}(x^{-1/3})^{2}dx = \int^{1}_{0}(x^{-2/3})dx = 3x^{1/3}|^{1}_{0} = 3[/tex]

    Since the solution exists then the function is in L2, correct?
     
  2. jcsd
  3. Aug 31, 2010 #2
    if that method is correct then it would not exist in L2(0,infinity), correct?
     
  4. Aug 31, 2010 #3

    lanedance

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    Homework Helper

    that all sounds reasonable to me, though i'm not an expert in these things
     
  5. Aug 31, 2010 #4

    Dick

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    Science Advisor
    Homework Helper

    Correct.
     
  6. Aug 31, 2010 #5
    Great, thanks!
     
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