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

Integral transforms - convergence

  1. Jun 4, 2008 #1

    I have a question which is most probably standard, but I don't have access to a textbook right now...

    Given a function [itex]K(y,x):\mathbb{R}^2\to\mathbb{R}[/itex] and a funtion [itex]f_0:\mathbb{R}\to\mathbb{R}[/itex], under what circumstances does the sequence [itex](f_n)_{n\geq0}[/itex] with
    f_n(x) = \int_{\mathbb{R}}{dy\, f_{n-1}(y)K(y,x)}

    I have a feeling [itex]|K(x,y)|<1[/itex] could be sufficient (maybe if one assumes that f_0 tends to zero fast enough...)


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

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