MacLane functions with prescribed zeros and interpolation properties

Abstract

An entire function ϕ is called universal in the sense of MacLane (for short MacLane function) if for any preassigned entire functionIt 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.