Talk:Aufgaben:Problem 14

What should this "Pierre's lemma" be? It's clearly false: Let \( f = u + iv \) (with \( u \) and \( v \) real-valued) be any non-constant analytic function; then clearly \( u \) or \( v \) is not constant. Following "Pierre's lemma" they should both be analytic, but we've showed in Ch. II.3 that any analytic real-valued function on a domain is constant, which is a contradiction. (And in any case, in the "proof" \( a \) and \( b \) should be different from \( 0 \)...)

Cheers, the tables