刊名:Journal of Mathematical Analysis and Applications
出版年:2016
出版时间:15 February 2016
年:2016
卷:434
期:2
页码:1091-1105
全文大小:391 K
文摘
Let ϕ(x)=∑αnxn be a formal power series with real coefficients, and let D denote differentiation. It is shown that “for every real polynomial f there is a positive integer m0 such that ϕ(D)mf has only real zeros whenever m≥m0” if and only if “α0=0 or ”, and that if ϕ does not represent a Laguerre–Pólya function, then there is a Laguerre–Pólya function f of genus 0 such that for every positive integer m , ϕ(D)mf represents a real entire function having infinitely many nonreal zeros.