Article
Dense-lineability of sets of Birkhoff-universal functions with rapid decay
Author/s | Bernal González, Luis
![]() ![]() ![]() ![]() ![]() ![]() ![]() Calderón Moreno, María del Carmen ![]() ![]() ![]() ![]() ![]() ![]() Luh, Wolfgang |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2010-03-01 |
Deposit Date | 2019-06-19 |
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Abstract | Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear ... Let A be an unbounded Arakelian set in the complex plane whose complement has infinite inscribed radius, and ψ be an increasing positive function on the positive real numbers. We prove the existence of a dense linear manifold M of entire functions all of whose nonzero members are Birkhoff-universal, such that each function in M has overall growth faster than ψ and, in addition, exp(|z|α)f(z) → 0 (z → ∞, z ∈ A) for all α < 1/2 and f ∈ M. With slightly more restrictive conditions on A, we get that the last property also holds for the action T f of certain holomorphic operators T. Our results unify, extend and complete recent work by several authors. |
Project ID. | FQM-127
![]() MTM2006-13997-C02-01 ![]() MTM2006-26627-E ![]() |
Citation | Bernal González, L., Calderón Moreno, M.d.C. y Luh, W. (2010). Dense-lineability of sets of Birkhoff-universal functions with rapid decay. Journal of Mathematical Analysis and Applications, 363 (1), 327-335. |
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