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

Inverse of a Definite Integral or integral transform

  1. Apr 8, 2012 #1
    Is there a general inversion formula or procedure for an integral of the form (where f is the function being transformed and g depends on the type of transform) [itex]\int[/itex][itex]^{a}_{b}[/itex] f(x) *g(x,[itex]\xi[/itex]) dx ?
    Inverses are defined in the conventional ways for functionals and integral transforms, respectively.

    For instance, for the fourier transform. In the equation above, a=∞,b=-∞, g(x,[itex]\xi[/itex])=[itex]e^{-2πix \xi }[/itex]. I know the inverse fourier transform is simple but I am concerned with a general procedure or process.

    I am most interested in the cases where a,b=±∞ although a simple inverse for [itex]\int[/itex][itex]^{a}_{b}[/itex] f(x) dx is also something I am curious about.

    Feel free to use complex analysis or any other branch of math if it helps to answer the question. Also, you can repost on another site if it will help.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted