Parseval frames from compressions of Cuntz algebras

被引：0

作者：

Christoffersen, Nicholas ^{[1
]}

Dutkay, Dorin Ervin ^{[2
]}

Picioroaga, Gabriel ^{[3
]}

Weber, Eric S. ^{[4
]}

机构：

[1] Univ Colorado, Dept Math, Campus POB 395,2300 Colorado Ave, Boulder, CO 80309 USA

[2] Univ Cent Florida, Dept Math, 4000 Cent Florida Blvd,POB 161364, Orlando, FL 32816 USA

[3] Univ South Dakota, Dept Math Sci, 414 E Clark St, Vermillion, SD 57069 USA

[4] Iowa State Univ, Dept Math, 396 Carver Hall,411 Morrill Rd, Ames, IA 50011 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2023年 / 304卷 / 01期

关键词：

Cuntz algebra; Parseval frame; Row co-isometry; Iterated function systems; Fourier series; Fractal measures; Walsh bases; FOURIER-SERIES;

D O I：

10.1007/s00209-023-03259-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A row co-isometry is a family (V-i)(i=0)(N-1) of operators on a Hilbert space, subject to the relation Sigma(N- 1)(i=0) ViV* (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.

引用

页数：36

共 29 条

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