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Markus Nieß

MacLane functions with prescribed zeros and interpolation properties

Keywords: spaces of entire functions, universality, approximation by derivatives, zeros, interpolation

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^(n_k) 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.

Analysis, Oldenbourg Wissenschaftsverlag

Print ISSN: 0174-4747
Volume: 27, 02/2007
Pages: 323 - 332

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