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arXiv · 2201.09714

Parseval Frames from Compressions of Cuntz Algebras

Nicholas Christoffersen·Dorin Ervin Dutkay·Gabriel Picioroaga·Eric Weber
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Abstract

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 \cite{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. \end{abstract}

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Nicholas Christoffersen, Dorin Ervin Dutkay, Gabriel Picioroaga, Eric Weber. 2022-01-24. Parseval Frames from Compressions of Cuntz Algebras. https://arxiv.org/abs/2201.09714

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