How Many Essentially Different Functional Theories Exist?

TL;DR

This paper explores the ambiguity in defining essentially different functional theories, clarifies key concepts, and introduces a new framework for analytic function theories based on group representations.

Contribution

It provides a clarified understanding of the concepts and proposes a novel framework for analytic function theories using group representations.

Findings

Clarified the ambiguity in defining different functional theories

Presented a new group representation-based framework for analytic functions

Discussed approaches to distinguish essentially different theories

Abstract

The question in the title is ambiguous. At least the understanding of words essentially different and function theory should be clarified. We discuss approaches to do that. We also present a new framework for analytic function theories based on group representations.