Extended point values of distributions

Abstract

An extension method for linear functionals is given. The proposed method provides extensions of a linear functional T defined on a subspace X of a vector space Y over a field K, by using a suitable isomorphism S : Y −→ Y that satisfies S (X) = X and TS = T. The extension Text : Xext −→ K is linear, and it is defined over a vector space Xext that contains X. Several illustrations are considered, including symmetric values, extension with respect to dilations, extended Cesàro summability of series, and extended multidimensional point values.