Parseval Frames from Compressions of Cuntz Algebras

A row co-isometry is a family$(V_i)_{i=0}^{N-1}$of operators on a Hilbert space, subject to the relation$$\sum_{i=0}^{N-1}V_iV_i^*=I.$$As shown in BJK00, row co-isometries appear as compressions of representations of Cuntz algebras. In this paper we will present some general constructions of Parseva...

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Bibliographic Details
Main Authors Christoffersen, Nicholas, Dutkay, Dorin Ervin, Picioroaga, Gabriel, Weber, Eric
Format Journal Article
LanguageEnglish
Published 24.01.2022
Subjects
Mathematics - Functional Analysis
Mathematics - Operator Algebras
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DOI10.48550/arxiv.2201.09714

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Summary:A row co-isometry is a family$(V_i)_{i=0}^{N-1}$of operators on a Hilbert space, subject to the relation$$\sum_{i=0}^{N-1}V_iV_i^*=I.$$As shown in BJK00, row co-isometries appear as compressions of representations of Cuntz algebras. In this paper we will present some general constructions of Parseval frames for Hilbert spaces, obtained by iterating the operators$V_i$on a finite set of vectors. The constructions are based on random walks on finite graphs. As applications of our constructions we obtain Parseval Fourier bases on self-affine measures and Parseval Walsh bases on the interval. abstract
DOI:10.48550/arxiv.2201.09714