Interpolation of Entire Functions and Projective Descriptions

Special entire functions of completely regular growth with additional properties are utilized to interpolate entire functions with certain bounds, and to give an example of a weighted inductive limit of Banach spaces of entire functions such that its topology cannot be described by the canonical weighted sup-seminorms associated with the weights of the steps. This provides a new, more natural counterexample to a problem of Bierstedt, Meise, and Summers