Article
A lot of “counterexamples” to Liouville's theorem
Author/s | Bernal González, Luis |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 1996-08-01 |
Deposit Date | 2019-06-19 |
Published in |
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Abstract | We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any ... We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j. Moreover, it is shown the existence of an entire function with infinite growth index satisfying the latter property. |
Project ID. | PB93-0926 |
Citation | Bernal González, L. (1996). A lot of “counterexamples” to Liouville's theorem. Journal of Mathematical Analysis and Applications, 201 (3), 1002-1009. |
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