Final sets for operators on real entire functions of order one, normal type

Abstract

Let f f be a real entire function of order one, normal type that is bounded on the real axis and L = φ ( D ) L = \varphi \left ( D \right ) , D = ( d / d z ) D = \left ( {d / dz} \right ) with φ ( ω ) \varphi \left ( \omega \right ) a Laguerre-Pólya function satisfying φ ( 0 ) = 0 \varphi \left ( 0 \right ) = 0 . Then the final set of f f with respect to L L is contained in the real axis as either a discrete subset or the whole axis.