Hermite-poulain Theorem in Finite Difference Setting
نویسنده
چکیده
In this note we attempt to develop an analog of Pólya-Schur theory describing the class of univariate hyperbolicity preservers in the setting of linear finite-difference operators. We study the class of linear finite-difference operators preserving the set of real-rooted polynomials whose mesh (i.e. the minimal distance between the roots) is at least one. In particular, finitedifference versions of the classical Hermite-Poulain theorem and its counterpart in finite degrees are obtained.
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تاریخ انتشار 2010