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!

Bergmann Space

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data

    If G = { z in C: 0<|Z|<1} show that every f in L_{a}^{2}(G) has a removable singularity at z = 0


    We must show that lim z->0 z*f(z) = 0 for all f in L_{a}^{2}(G)

    By a corollary 1.12, if f in L_{a}^{2}(G), a in G and 0<r<dist(a,bdr G), thne
    |f(a)| <= 1/(r\sqrt(\pi))||f||_2,

    for |z| < 1/2 we have that

    |f(z)| <= 1/(|z|\sqrt(pi)/sqrt(2)) ||f||_2 = 2/(|Z|sqrt(pi) ||f||_2

    so that |zf(z)| = |z||f(z)| <= 2/sqrt(pi) ||f||_2.

    how do I proceed from there

    2. Relevant equations

    3. The attempt at a solution
  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?

Similar Discussions: Bergmann Space
  1. Complete measure space (Replies: 0)