Talk:Positive harmonic function

Question on the proof of Carathéodory's criterion
How do you prove the following equation?
 * $$\sum_{m=0}^\infty\sum_{n=0}^\infty a_{m-n} \lambda_m\overline{\lambda_n} = 2(1-|z|^2) \,\Re\, f(z).$$

Thanks! Zatrp (talk) 23:00, 21 April 2014 (UTC)


 * My impression is that it just can't be right because the right-hand-side does not depend on the constants $$a_n$$. This is an important problem because the identity is used in the proof of Carathéodory's criterion in this article. Zatrp (talk) 10:19, 13 May 2014 (UTC)