Parseval Frames from Compressions of Cuntz Algebras - Christoffersen, Nicholas; Dutkay, Dorin Ervin; Picioroaga, Gabriel; Weber, Eric (2022)
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