On identity theorem for real functions

TL;DR

This paper extends the identity theorem from complex analytic functions to certain classes of real analytic functions, providing conditions under which these functions are uniquely determined by their values on specific sets.

Contribution

It introduces sufficient conditions for real analytic functions to satisfy an identity theorem analogous to the complex case, expanding understanding of function uniqueness.

Findings

Established conditions for real analytic functions to satisfy an identity theorem

Extended the concept of function uniqueness from complex to real analytic functions

Provided theoretical framework for future research in real function analysis

Abstract

Identity theorem for analytic complex functions says that a function is uniquely defined by its values on a set that contains a density point. The paper presents sufficient conditions for classes of real analytic functions that ensures similar property.