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Linear Differential Operator/Inner Product

  1. May 19, 2009 #1
    Can anyone help me?

    Q. An inner product is defined on the vector space V of all (real) polynomials (of arbitrary
    degree) by


    Show that the linear differential operator


    is symmetric with respect to this inner product.

    Don't necessarily need the exact answer, just need to know how I'm meant to go about it.
    Last edited: May 19, 2009
  2. jcsd
  3. May 19, 2009 #2


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    Science Advisor

    Let f and g be a polynomials. Show that <Lf, g>= <f, Lg>.
  4. May 19, 2009 #3
    Ah right, thanks.

    So all I need to do is replace the f(x) in the integral with Lf(x) (and the same with g(x) on the other side)? I'll give it a go anyway. Cheers.
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