Let <mi mathvariant="normal">&#x03A9;<!-- Ω --> &#x2282;<!-- ⊂ --> <mrow class="MJX-TeXAto

Ayanna Trujillo

Ayanna Trujillo

Answered question

2022-06-24

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 .

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?