Cuntz-Krieger algebras and wavelets on fractals

2009/08/05 by Matilde Marcolli, Marcolli, Matilde, A. M. Paolucci +1 · 2 citations
Mathematics · #28A80 #42C40 #46L85 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.0908.0596

openalex publication_date 2009/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider representations of Cuntz--Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron-Frobenius and Ruelle operators to construct families of wavelets on these Cantor sets.

Cited by

• Relative ultragraph algebras and infinite interval maps
• Error-correcting codes and phase transitions

Related

• Wavelets and spectral triples for fractal representations of Cuntz algebras
• Compactly supported wavelets and representations of the Cuntz relations
• Closed subspaces which are attractors for representations of the Cuntz algebras
• Wavelets in mathematical physics: q-oscillators
• Representations of Cuntz algebras, loop groups and wavelets