Abstract
Let K be a compact convex set in C. For each point zO ε ∂K and each holomorphic polynomial p = p(z) having all of its zeros in K, we prove that there exists a point z ε K with |z -zO| ≤ 20 diam K/ √deg p such that |p′(z)| ≥ (deg p)1/2/20(diam K) |p(zO)| i.e., we have a pointwise reverse Markov inequality. In particular, ∥p′∥k ≥ (deg p)1/2/20(diam K)∥p∥k.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 173-182 |
| Number of pages | 10 |
| Journal | Annales Academiae Scientiarum Fennicae Mathematica |
| Volume | 27 |
| Issue number | 1 |
| State | Published - 2002 |
ASJC Scopus subject areas
- General Mathematics