Partial Classification of Polynomials and an Orthonormal Basis Construction on the Associated Basin of Attraction
James Tipton
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.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Mathematical functions and polynomials · Matrix Theory and Algorithms
\usetkzobj
all
Research Papers
James Tipton
Partial Classification of Polynomials and an Orthonormal Basis Construction on the Associated Basin of Attraction
James Tipton