Abstract

Let ϕ and f be functions in the Laguerre–Pólya class. Write ϕ ( z ) = e − α z 2 ϕ 1 ( z ) and f ( z ) = e − β z 2 f 1 ( z ) , where ϕ 1 and f 1 have genus 0 or 1 and α , β ⩾ 0 . If α β < 1 / 4 and ϕ has infinitely many zeros, then ϕ ( D ) f ( z ) has only simple real zeros, where D denotes differentiation.

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