A lot of "counterexamples" to Liouville's theorem

Description

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.

Abstract

Dirección General de Investigación Científica y Técnica (DGICYT). España

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