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Hilbert Space Help!

  1. Sep 19, 2005 #1
    How can I show that the space of all continuously differentiable functions on [a,b] denoted W[a,b] with inner product (f,g)=Integral from a to b of (f(x)*conjugate of g(x)+f'(x)*conjugate of g'(x)).

    Should I show that the norm does not satisfy the parallelogram law?
  2. jcsd
  3. Sep 19, 2005 #2


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    What do you want to show ?

    And just to clarify, you have the inner product defined as :

    [tex] \langle f,g \rangle = \int _a ^b (fg^* + f'g'^*)dx [/tex] ?
  4. Sep 19, 2005 #3
    I think I need to show that W[a,b] is not a complete metric space?

    And yes that is right inner product.
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