{"paper":{"title":"Order of growth of distributional irregular entire functions for the differentiation operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antonio Bonilla, Luis Bernal-Gonzalez","submitted_at":"2015-08-28T12:16:05Z","abstract_excerpt":"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) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07177","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}