This article is cited in 6 papers

The Dirichlet Ring and Unconditional Bases in $L_2[0,2\pi]$

A. Sowa

Department of Mathematics and Statistics, University of Saskatchewan, Canada

Abstract: It is observed that the Dirichlet ring admits a representation in an infinite-dimensional matrix algebra. The resulting matrices are subsequently used in the construction of nonorthogonal Riesz bases in a separable Hilbert space. This framework enables custom design of a plethora of bases with interesting features. Remarkably, the representation of signals in any one of these bases is numerically implementable via fast algorithms.

Keywords: unconditional basis, Riesz basis, fast transform, Dirichlet series.

UDC: 517.98

Received: 06.06.2011

DOI: 10.4213/faa3113

 English version: Functional Analysis and Its Applications, 2013, 47:3, 227–232

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