1. Not finding help here? Sign up for a free 30min 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!

Fourier transform conjucture/theorem

  1. Apr 20, 2008 #1
    fourier transform conjecture/theorem

    Is this a theorem?

    Let [itex]f\in L^2(\mathbb{R},\mathbb{R})[/itex] be such function that f is continuous on some sets [itex]]x_0-\delta, x_0[[/itex] and [itex]]x_0, x_0+\delta[[/itex] with [itex]\delta >0[/itex], and

    \lim_{x\to x_0^-} f(x) \neq \lim_{x\to x_0^+}f(x).

    (So we cannot choose a continuous g such that [g]=[f] in [itex]L^2[/itex] sense)

    There does not exist such [itex]M,C,\epsilon>0[/itex], that

    |(\mathcal{F} f)(k)| < C \frac{1}{|k|^{1+\epsilon}},\quad \forall |k|> M.
    Last edited: Apr 20, 2008
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Fourier transform conjucture/theorem
  1. Fourier transform (Replies: 2)

  2. Fourier transforms (Replies: 1)

  3. Fourier transform (Replies: 1)