Abstract
Eremenko and Lyubich proved that an entire function ƒ
whose set of singular values is bounded is expanding at points where ƒ (z)
is large. These expansion properties have been at the centre of the subsequent study of this class of functions, now called the Eremenko–Lyubich class. We improve the estimate of Eremenko and Lyubich, and show that the new estimate is asymptotically optimal. As a corollary, we obtain an elementary proof that functions in the Eremenko–Lyubich class have lower order at least 1/2.
.
whose set of singular values is bounded is expanding at points where ƒ (z)
is large. These expansion properties have been at the centre of the subsequent study of this class of functions, now called the Eremenko–Lyubich class. We improve the estimate of Eremenko and Lyubich, and show that the new estimate is asymptotically optimal. As a corollary, we obtain an elementary proof that functions in the Eremenko–Lyubich class have lower order at least 1/2.
.
| Original language | English |
|---|---|
| Pages (from-to) | 113-118 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 55 |
| Issue number | 1 |
| Early online date | 29 Jul 2022 |
| DOIs | |
| Publication status | Published - 1 Feb 2023 |