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A Lot of “Counterexamples” to Liouville's Theorem

✍ Scribed by Luis Bernal-González

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
122 KB
Volume
201
Category
Article
ISSN
0022-247X

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✦ Synopsis

We prove in this paper that, given ␣ g 0, 1r2 , there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions Ž< < ␣ . Ž j. Ž . and, in addition, lim exp z f z s0 on any plane strip for every f g M z ª ϱ and for every derivation index j. Moreover, it is shown the existence of an entire function with infinite growth index satisfying the latter property.

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