The growth at infinity of a sequence of entire functions of bounded orders
| dc.creator | Trong, Dang Duc | |
| dc.creator | Tuyen, Truong Trung | |
| dc.date | 2007-11-19 | |
| dc.date | 2007-11-21 | |
| dc.date.accessioned | 2026-07-07T08:43:54Z | |
| dc.date.available | 2026-07-07T08:43:54Z | |
| dc.description | In this paper we shall consider the growth at infinity of a sequence $(P_n)$ of entire functions of bounded orders. Our results extend the results in \cite{trong-tuyen2} for the growth of entire functions of genus zero. Given a sequence of entire functions of bounded orders $P_n(z)$, we found a nearly optimal condition, given in terms of zeros of $P_n$, for which $(k_n)$ that we have \begin{eqnarray*} \limsup_{n\to\infty}|P_n(z)|^{1/k_n}\leq 1 \end{eqnarray*} for all $z\in \mathbb C$ (see Theorem \ref{theo5}). Exploring the growth of a sequence of entire functions of bounded orders lead naturally to an extremal function which is similar to the Siciak's extremal function (See Section 6). | |
| dc.description | 19 pages. Some typos are corrected | |
| dc.identifier | https://arxiv.org/abs/0711.2808 | |
| dc.identifier | http://arxiv.org/abs/0711.2808 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142478 | |
| dc.subject | Complex Variables | |
| dc.subject | 30C85, 30D15, 31A15 | |
| dc.title | The growth at infinity of a sequence of entire functions of bounded orders | |
| dc.type | text |