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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Analysis is devoted to the field of mathematical analysis, in particular classical analysis and its applications. Its aim is to publish the best research articles within the scope of the journal, as well as to boost the cooperation between scholars.

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