On the convergence of certain basic sets of polynomials

Abstract

In this paper, various problems relating to the properties of the Hadamard set of simple basic sets of polynomials are treated with particular emphasis on distinction between the single and several complex variables cases. An important result is established for the relationship between the Cannon functions of simple sets of polynomials in several complex variables and those of the directly Hadamard sets. Possible results on the effectiveness of Hadamard set for several complex variables at the origin are also discussed.