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Hilbert schmidt norm

  1. Dec 3, 2008 #1
    1. The problem statement, all variables and given/known data

    http://img523.imageshack.us/img523/4456/56166304yr3.png [Broken]

    2. Relevant equations
    http://img356.imageshack.us/img356/2793/40249940is8.png [Broken]

    3. The attempt at a solution
    I defined K:[a,b] --> [a,b] with [tex] k(s,t) = \frac{(t-s)^{n-1}}{(n-1)!} [/tex]

    I found for the norm:

    [tex] \int_a^b \int_a^b \frac{(t-s)^{2n-2}}{(n-1)!^2}\ \mbox{d}s\ \mbox{d}t =0[/tex]

    Is this correct?
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Dec 3, 2008 #2


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    If the norm of blah is zero, then blah is zero. Is blah zero in this case?
  4. Dec 4, 2008 #3
    You're right something is wrong.

    But is the integral set up with the correct boundaries?
  5. Dec 5, 2008 #4
    Ok presuming the boundaries are ok I end up with:

    [tex]||A||_{HS} = \frac{2 (b-a)^n}{((n-1)!)^2 (2n-1)(2n)} [/tex]

    Is this correct?
  6. Dec 5, 2008 #5


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    Did you remember to take the square root?
    Last edited: Dec 5, 2008
  7. Dec 5, 2008 #6
    You might want to include some characteristic function like [itex]\chi_{\{s\leq t\}}[/itex] in your kernel function.
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