Holomorphic Extension Theorem for Tempered Ultrahyperfunctions

TL;DR

This paper establishes a holomorphic extension theorem for tempered ultrahyperfunctions associated with convex cones, extending classical results and providing applications to analytic function determination and generalizations of Martineau's theorem.

Contribution

It introduces a holomorphic extension theorem for tempered ultrahyperfunctions in convex cones, extending the edge of the wedge theorem and related principles.

Findings

Proves a holomorphic extension theorem for tempered ultrahyperfunctions.

Provides a principle for determining analytic functions from real sets.

Generalizes Martineau's holomorphic extension theorem.

Abstract

In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated edge of the wedge theorem) will be given for this setting. As application, a version is also given of the principle of determination of an analytic function by its values on a non-empty open real set. The paper finishes with the generalization of holomorphic extension theorem \`a la Martineau.