A Generalization, to Higher Dimensions, of a Theorem of Lucas Concerning the Zeros of the Derivative of a Polvnomial of one Complex Variable

Abstract

Let m and n be positive integers, and z₁,z₂,...,z_m be m points in real n dimensional Euclidean space E_n, For eachj=1,2,...,m,let f_j be a real valued continuously differentiate function of the positive real variable r, with f_j(r)gt;0 for r>0, Consider the real valued function F, which is defined, for w in E_n, with w=z_j forj = 1,2,..., m, by the equation

^†The research of this author was supported by NSF Grant GP-23504. Presented by this at the International Congress of Mathematicias Vaneouver.Canada.1974.

^†The research of this author was supported by NSF Grant GP-23504. Presented by this at the International Congress of Mathematicias Vaneouver.Canada.1974.

Notes

^†The research of this author was supported by NSF Grant GP-23504. Presented by this at the International Congress of Mathematicias Vaneouver.Canada.1974.