there may be an train in a e-book on advanced evaluation:
“Let f is a holomorphic perform on C such that exists a>zero with property f(z) = f(z+a) = f(z+ja)
for every z in C. Present, that f should be essentially fixed.”
The trace is to make use of Liuville theorem: “Each bounded complete perform should be fixed. That’s, each holomorphic perform f for which there exists a constructive quantity M such that |f(z)|<=M for all z in C is fixed.”
So to complete the train it suffices to indicate f(z) is bounded for all z in C. May somebody assist me? Or miss i one thing trivial?
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