Harmonic analysis of iterated function systems with overlap
Palle E. T. Jorgensen, Keri A. Kornelson, Karen L. Shuman
TL;DR
This paper extends harmonic analysis techniques to iterated function systems with overlaps using operator systems that generalize Cuntz relations, bridging operator algebra and signal processing.
Contribution
It introduces a novel operator framework for analyzing overlapping IFSs, expanding the scope of harmonic analysis in fractal and dynamical systems.
Findings
Developed a new operator system approach for overlapping IFSs
Extended harmonic analysis methods to systems with overlaps
Bridged concepts from operator algebra and signal processing
Abstract
In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.
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.