Analytic continuation from a family of lines

TL;DR

This paper proves that if a function defined outside a convex curve in the plane extends as entire functions along tangent lines, then it is globally an entire function of two variables.

Contribution

It establishes a new analytic continuation result linking tangent line extensions to the global analyticity of functions in the plane.

Findings

Functions extendable along tangent lines are entire in the plane.

The result applies to functions outside convex curves.

Provides conditions for global analyticity from line restrictions.

Abstract

Given a function f in the exterior of a convex curve in the real plane, we prove that if the restrictions of f to the tangent lines to the curve extend as entire functions, then the function f is an entire function of two variables.