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Hilbert Space

  1. May 30, 2010 #1
    Hilbert Space....

    Can somebody tell me the difference between H1 & H2 hilbert spaces?
  2. jcsd
  3. May 30, 2010 #2


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    Re: Hilbert Space....

    These are two special Sobolev spaces, namely

    [tex]H^k = W^{k,2}[/tex]

    The "2" refers to the usual norm of the [tex]L^2[/tex] Hilbert space. The "k" means that instead of the function [tex]f(x)[/tex] one considers in addition its first, second, ..., kth derivative:

    [tex]||f||^2_{H^k} = ||f||^2_{W^{k,2}} = \sum_{i=0}^k\int dt\,|f^{(i)}|^2[/tex]
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