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Ayanna Trujillo

Ayanna Trujillo

Answered question


Let Ω C be a bounded domain which does not contain any pole of a rational function R and R ( z ) 0 for all z Ω. Is it true that R ( z ) is injective on Ω?

Answer & Explanation

Quinn Everett

Quinn Everett

Beginner2022-06-25Added 23 answers

No; consider R ( z ) = z n for some n 2 and Ω a neighborhood of a sufficiently long arc of the unit circle S 1 C .

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