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Interpolation of entire functions and projective descriptions. (English) Zbl 0992.46002
Summary: 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 product of Bierstedt, Meise, and Summers.

MSC:
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46M40 Inductive and projective limits in functional analysis
32A15 Entire functions of several complex variables
46E10 Topological linear spaces of continuous, differentiable or analytic functions
32E30 Holomorphic, polynomial and rational approximation, and interpolation in several complex variables; Runge pairs
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