Orthonormal bases generated by Cuntz algebras
Dorin Ervin Dutkay, Gabriel Picioroaga, Myung-Sin Song
TL;DR
This paper demonstrates how various orthonormal bases, including Fourier, Walsh, and exponential bases, can be constructed using representations of the Cuntz algebra, linking algebraic structures to functional bases on fractals.
Contribution
It introduces a unified approach to generate diverse orthonormal bases via Cuntz algebra representations, expanding the understanding of bases on fractal measures.
Findings
Constructed Fourier bases on fractal measures.
Developed generalized Walsh bases on the unit interval.
Created piecewise exponential bases on the middle third Cantor set.
Abstract
We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical Dynamics and Fractals · Advanced Operator Algebra Research