Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Generalized version of the Fourier Transform

  1. Aug 31, 2016 #1
    Hello everyone,

    I was trying to develop a sort of generalized version of the Fourier Transform. My question in particular is:
    Given a function [itex]f(x,u)[/itex], is there a function [itex]g(x,u)[/itex] with [tex]\int_{-\infty}^\infty f(x,u)g(x,u')\mathrm{d}x=\delta(u-u')[/tex]

    For [itex]f(x,u)=e^{2\pi ixu}[/itex] the solution would be [itex]g(x,u)=\frac{1}{2\pi}e^{-2\pi ixu}[/itex]. Are there other pairs with this property?

    Thank you for your help :)
  2. jcsd
  3. Aug 31, 2016 #2

    Dr Transport

    User Avatar
    Science Advisor
    Gold Member

    look at the theory of Sturm-Liouville functions
  4. Aug 31, 2016 #3


    User Avatar
    Science Advisor

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Generalized version of the Fourier Transform
  1. Fourier transform? (Replies: 3)

  2. Fourier Transformations (Replies: 10)

  3. Fourier Transform (Replies: 5)