Difference between revisions of "Talk:Aufgaben:Problem 14"
From Ferienserie MMP2
(Created page with "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 functions; then u and v are...") |
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What should this "Pierre's lemma" be? It's clearly false: | 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 | + | Let \( f = u + iv \) (with \( u \) and \( v \) real-valued) be any non-constant analytic function; then \( u \) and \( v \) are not constant. Following "Pierre's lemma" they should 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 | Cheers, the tables | ||
Revision as of 13:42, 31 December 2014
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 \( u \) and \( v \) are not constant. Following "Pierre's lemma" they should 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
