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Beyond distribution theory

  1. Oct 5, 2009 #1
    given a differentiable function g(x) we know that in many cases if we define [tex] g(nx) [/tex] for n--> oo , then we have no longer a function but a DISTRIBUTION

    example [tex] \delta (x) = \frac{sin(Nx)}{x} [/tex] as n--->oo

    could the same be applied in distribution theory ? for example

    [tex] T(n,x)= \sum_{i=0}^{n}\delta (x-i) [/tex]

    and for the complex integration could we consider

    [tex] \int_{C}dsF(s)x^{s}/s [/tex] ,

    here F(s) is a test function in complex plane and [tex] x^{s}/s [/tex] is a distribution on parameter 's' , and x is a real constant.
  2. jcsd
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