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)