Parseval frames from compressions of Cuntz algebras - Christoffersen, Nicholas; Dutkay, Dorin Ervin; Picioroaga, Gabriel; Weber, Eric S. (Mathematische Zeitschrift, 2023)
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 - 1 V i V i ∗ = I . As shown in Bratteli et al. (J Oper Theory, 43, 97–143, 2000), 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.