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

Dividing both sides by a Dirac delta function - ok?

  1. Sep 8, 2010 #1
    Suppose I wind up with the relation

    [tex]f(x)\delta (x-x')=g(x)\delta (x-x')[/tex]

    true for all x'.

    Can I safely conclude that f(x) = g(x) (for all x)? Or am I overlooking something? this is a little too close to dividing both sides by zero for comfort.
    Last edited: Sep 8, 2010
  2. jcsd
  3. Sep 8, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    You could integrate your relation over any interval containing x, and use the definition of the delta function (or rather, distribution):

    f(x)\delta (x-x')=g(x)\delta (x-x')
    [tex]\int_{x - \epsilon}^{x + \epsilon} f(x)\delta (x-x') \, \mathrm{d}x' = \int_{x - \epsilon}^{x + \epsilon} g(x)\delta (x-x') \, \mathrm{d}x'
    which evaluates (by definition of the delta) to
    [tex]f(x) = g(x)[/tex]
  4. Sep 8, 2010 #3
    Thank you!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Dividing both sides Date
I Dividing Complex Numbers Jan 21, 2018
B If a divides b^2, a divides b Apr 12, 2017
B Squaring both sides of an equation? Mar 24, 2017
I Newton Divided Difference Interpolation Polynomial Feb 8, 2017
B Is infinity a prime number? Nov 4, 2016