Small entire functions with extremely fast growth

[摘要] We prove in this note that, given alpha is an element of (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions such that lim(z-->infinity)exp(\z\(alpha))f((j))(z) = 0 on any plane strip for every f is an element of M and for every derivation index j. Moreover, the growth index of each nonnull function of M is infinite with respect to any prefixed sequence of nonconstant entire functions. (C) 1997 Academic Press.

[发布日期] 1997-03-15