Gurko I. Balikov
Notes on the continuous linear extension operator and the basis in some DFS-spaces of ultradifferentiable functions on interval
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 52, 47-56 (1998)

MSC:

46E10 Topological linear spaces of continuous, differentiable or analytic functions

Abstract: We consider relation between a basis and continuous linear extension operator of the functions from outside a interval.

This work considers DFS-spaces\footnote[2]{An inductive limit of F spaces
with compact embedding operator.} of ultradifferentiable functions on interval.
Unlike the results of R.Meise's and A.Taylor's works [8,9], we give a method
for concretely construction of continuous linear extension operator.
We also considered the relations between a basis and a continuous
linear extension operator of the functions outside an interval.
Keywords: Topological linear spaces of continuous, differentiable or analytic functions