Characterization of distributions having a value at a point in the sense of Robinson

TL;DR

This paper characterizes Schwartz distributions with a point value in Robinson's nonstandard analysis sense, showing they are continuous near that point, thus linking point values to local continuity properties.

Contribution

It provides a novel characterization of distributions with point values using nonstandard analysis, connecting pointwise values to local continuity.

Findings

Distributions with a point value are continuous near that point.

The characterization uses Robinson's nonstandard analysis framework.

This links pointwise values to local regularity of distributions.

Abstract

We characterize Schwartz distributions having a value at a single point in the sense introduced by means of nonstandard analysis by A. Robinson. They appear to be distributions continuous in a neighborhood of the point.