
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 testfunction $\displaystyle \phi$ we have like $\displaystyle \left\langle u_{t,N},\phi \right\rangle = i \phi(0)t^{N1} + i\left\langle u_{t,N1},\phi' \right\rangle $ by partial integration. (at least that is what Ive got....) . So how do we solve the distributional limit? Whats the idea...