On Theorems of Walsh and Laguerre Concerning Zeros of Polynomials PDF

Keywords

mathematics, null-sets, polynomials

Abstract

We obtain a general theorem on the location of null-sets of certain types of abstract polynomials in vector spaces of arbitrary dimension (finite, or otherwise). This theorem generalizes Walsh’s two-circle theorem concerning the critical points of rational functions of the form f/g, where f and g are complex-valued polynomials of the same degree; and it offers an extension of Laguerre’s theorem on polar-derivatives