Polynomial Form of de Branges Conditions for the Denseness of Algebraic Polynomials in the Space $C_w^0$

Abstract

In the criterion for polynomial denseness in the space $C_w^0$ established by de Brange in 1959, we replace the requirement of the existence of an entire function by an equivalent requirement of the existence of a polynomial sequence. We introduce the notion of strict compactness of polynomial sets and establish sufficient conditions for a polynomial family to possess this property.