Parseval Frames from Compressions of Cuntz Algebras

2022/01/24 by Christoffersen, Nicholas, Dutkay, Dorin Ervin, Picioroaga, Gabriel +1 · 1 citation
#05C81 #28A80 #42A16 #42C10 #47L55 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2201.09714

Abstract

A row co-isometry is a family (V_i)_i=0^N-1 of operators on a Hilbert space, subject to the relation ∑_i=0^N-1V_iV_i^*=I. As shown in \citeBJK00, 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. \endabstract

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