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Results tagged with cv.complex-variables
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user 127229
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
3
votes
0
answers
153
views
An inequality with rotation
Let $P(z)=\sum_{m=0}^na_mz^m$ be a polynomial of degree $n\geq 1$ having no zeros in $|z|<1,$ then for any complex number $\alpha$ with $|\alpha|=1,$ is it true on $|z|=1$ that
$$\left|\alpha zP'(z) …
- 83
4
votes
1
answer
364
views
Induction principle on proving an inequality
If $P(z)$ having no zeros in $|z|<1,$ then
$$\frac{\max_{|z|=1}|P'(z)|}{\max_{|z|=1}|P(z)|}\leq \frac{n}{2}.$$
Can we prove this by induction on $n$? or is there any alternative way?
Attempt at a …
- 83