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Small Entire Functions with Extremely Fast Growth

✍ Scribed by Luis Bernal-González

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
169 KB
Volume
207
Category
Article
ISSN
0022-247X

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✦ Synopsis

We prove in this note that, given ␣ g 0, 1r2 , there exists a linear manifold M M of entire functions satisfying that M M is dense in the space of all entire functions Ž< < ␣ . Ž j. Ž . such that lim exp z f z s0 on any plane strip for every f g M M and for z ª ϱ every derivation index j. Moreover, the growth index of each nonnull function of M M is infinite with respect to any prefixed sequence of nonconstant entire functions.

📜 SIMILAR VOLUMES

Small Entire Functions with Infinite Gro
Small Entire Functions with Infinite Growth Index
✍ A. Bonilla 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 69 KB

In this paper, we prove that given µ > 0 there exists a dense linear manifold M of entire functions, such that, lim z→∞ z∈l exp z µ f z = 0 for every f ∈ M and l straight line and with infinite growth index for all non-null functions of M. Moreover, every non-null function of M has exactly 2 2µ + 1