# Partial Classification of Polynomials and an Orthonormal Basis Construction on the Associated Basin of Attraction

## TL;DR

This paper classifies certain polynomials related to Fatou sets and introduces a method for constructing orthonormal bases in associated Hilbert spaces, advancing understanding of function iteration and kernel representations.

## Contribution

It offers a partial classification of polynomials suitable for a specific orthonormal basis construction method in Fatou set Hilbert spaces.

## Key findings

- Classified polynomials applicable to the basis construction
- Established conditions for the method's applicability
- Enhanced understanding of Fatou set Hilbert spaces

## Abstract

In the paper "Infinite product representations for kernels and iterations of functions", the authors associate certain Fatou subsets with reproducing kernel Hilbert spaces. They also present a method for constructing an orthonormal basis for said Hilbert space, but the method depends on the polynomial of the given Fatou set. We provide a partial classification of those polynomials the method applies to.