Sectorial Paley-Wiener Theorem

TL;DR

This paper proves a sectorial Paley-Wiener theorem extending classical results to functions of exponential type within sectors, improving previous bounds on analytic continuation.

Contribution

It corrects, simplifies, and extends Morimoto's result, establishing a maximal convex set for analytic continuation inside sectors.

Findings

Established a sectorial Paley-Wiener theorem for exponential type functions.

Identified the maximal convex set of analytic continuation in a sector.

Extended and improved previous results by Dzhrbashyan and Avetisyan.

Abstract

By correcting, simplifying and extending a result of Morimoto, we prove a Paley-Wiener type theorem for functions of exponential type in a sector. It serves as a sectorial analogue of Polya's theorem on the indicator of entire functions and improves a result of Dzhrbashyan and Avetisyan by finding the maximal convex set of analytic continuation inside a sector.