MacLane functions with prescribed zeros and interpolation properties

Markus Nieß

An entire function ϕ is called universal in the sense of MacLane (for short MacLane function) if for any preassigned entire function f a suitable sequence ϕ(nk) of derivatives of ϕ converges to f locally uniformly in the whole plane.

It is shown that for every appropriate choice of designated zeros in ℂ, there exists a MacLane function having zeros exactly in these points, of preassigned order. Moreover, there exist MacLane functions satisfying an interpolation problem in addition.

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