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arXiv · 1508.07177

Order of growth of distributional irregular entire functions for the differentiation operator

Luis Bernal-Gonzalez·Antonio Bonilla
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Abstract

We study the rate of growth of entire functions that are distributionally irregular for the differentiation operator D. More specifically, given $p \in [1,\infty ]$ and $b \in (0,a)$, where $a = \frac{1}{2 max\{2,p\}}$, we prove that there exists a distributionally irregular entire function $f$ for the operator D such that its p-integral mean function $M_p(f,r)$ grows not more rapidly than $e^r r^{-b}$. This completes related known results about the possible rates of growth of such means for D-hypercyclic entire functions. It is also obtained the existence of dense linear submanifolds of H(C) all whose nonzero vectors are D-distributionally irregular and present the same kind of growth.

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Luis Bernal-Gonzalez, Antonio Bonilla. 2015-08-28. Order of growth of distributional irregular entire functions for the differentiation operator. https://arxiv.org/abs/1508.07177

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