Artículo
Order of growth of distributional irregular entire functions for the differentiation operator
Autor/es | Bernal González, Luis
Bonilla Ramírez, Antonio Lorenzo |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2016 |
Fecha de depósito | 2016-11-11 |
Publicado en |
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Resumen | We study the rate of growth of entire functions that are distributionally
irregular for the differentiation operator D. More specifically, given p ∈ [1,∞]
and b ∈ (0, a), where a = 1 / 2 max{2, p}, we prove that there ... We study the rate of growth of entire functions that are distributionally irregular for the differentiation operator D. More specifically, given p ∈ [1,∞] and b ∈ (0, a), where a = 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 Mp(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. |
Identificador del proyecto | FQM-127
P08-FQM-03543 info:eu-repo/grantAgreement/MINECO/MTM2012-34847-C02-01 info:eu-repo/grantAgreement/MINECO/MTM2014-52376-P |
Cita | Bernal González, L. y Bonilla Ramírez, A.L. (2016). Order of growth of distributional irregular entire functions for the differentiation operator. Complex Variables and Elliptic Equations, 61 (8), 1176-1186. |
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