An inequality for the distribution of zeros of polynomials and entire functions

Abstract

An inequality is established which provides a unifying principle for the distribution of zeros of real polynomials and certain entire functions. This inequality extends the applicability of multiplier sequences to the class of all real polynomials. The various consequences obtained generalize and supplement several results due to Hermite-Poulain, Laguerre, Marden, Obreschkoff, Polya and Schur. 1* Introduction* In the vast literature dealing with the distribution of zeros of real polynomials and real entire functions, an important role is played by linear transformations T which possess the following property: (1)