1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A question on integral equations

  1. Sep 24, 2003 #1
    Let be the integral equation:

    f(x)-g(x)=Kf where K is the integral operator having the kernel

    my question : is there an operator R satisfying:

    g(x)-f(x)=Rg where f satisfy the original integral equation so it can be solved by mean of R operator.

    Another question is can any integral equation be transformed into a differential equation?..if so how it is made?..thanks.
  2. jcsd
  3. Sep 24, 2003 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member


    Just using algebra, I get:

    1. f(x)-g(x)=Kf(x)
    2. f(x)-Kf(x)=g(x)
    3. (1-K)f(x)=g(x)
    4. f(x)=(1-K)-1g(x)
    5. g(x)-f(x)=[1-(1-K)-1]g(x)

    Defining R as [1-(1-K)-1] seems to fit the bill. The only thing I am not sure of is whether (1-K) is invertible. I assumed that it was invertible in Step 4.

    edit: fixed bracket
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook