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Thread: Distributional limit

  1. #1
    Senior Member Dinkydoe's Avatar
    Dec 2009

    Distributional limit

    Hoi, im little new on functional analysis stuff...and I want to calculate the distributional limit of $\displaystyle u_{t,N}(x)= e^{itx}t^N$ defined for $\displaystyle x\geq 0$ and $\displaystyle u_{t,N}(x)=0$ elsewhere. So for any test-function $\displaystyle \phi$ we have like $\displaystyle \left\langle u_{t,N},\phi \right\rangle = i \phi(0)t^{N-1} + i\left\langle u_{t,N-1},\phi' \right\rangle $ by partial integration. (at least that is what Ive got....) . So how do we solve the distributional limit? Whats the idea...
    Last edited by Dinkydoe; Feb 18th 2013 at 01:33 AM.
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