Bernal González, Luis2019-06-192019-06-191996-08-01Bernal González, L. (1996). A lot of “counterexamples” to Liouville's theorem. Journal of Mathematical Analysis and Applications, 201 (3), 1002-1009.0022-247Xhttps://hdl.handle.net/11441/87504We 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Liouville’s theoremEntire functionsDense linear manifoldRadon transformArakelian setStrips and sectorsGrowth indexinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1006/jmaa.1996.0298