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- Title
Parseval frames from compressions of Cuntz algebras.
- Authors
Christoffersen, Nicholas; Dutkay, Dorin Ervin; Picioroaga, Gabriel; Weber, Eric S.
- 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 - 1 V i V i ∗ = I. <graphic href="209_2023_3259_Article_Equ36.gif"></graphic> 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.
- Subjects
RANDOM walks; ALGEBRA; REPRESENTATIONS of algebras; FOURIER series
- Publication
Mathematische Zeitschrift, 2023, Vol 304, Issue 1, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-023-03259-w