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!

Searching for a Counter-Example

  1. Oct 30, 2006 #1
    Hi,

    I am searching for a counter-example in analysis.
    Here is the problem :

    I want a differentiable (in the sense of [tex]R^2[/tex]) function [tex] f : \mathbb{C} \to \mathbb{C}[/tex] such that

    1) f is square integrable
    2) [tex]\partial_z f [/tex] is square integrable
    3) [tex]\partial_{\bar z} f [/tex] is not square integrable

    I tried, but I didnt find anything... Except the function [tex]f(z) = \bar z [/tex], which
    is such that 2) and 3) are satisfied, but 1) is not...

    Help...
     
  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



Similar Discussions: Searching for a Counter-Example
  1. Site Search (Replies: 2)

  2. Search algorithm (Replies: 14)

Loading...