Geodesic
The Dirichlet Ring and Unconditional Bases in $L_2[0,2\pi]$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 75-81.

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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. 
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A. Sowa. The Dirichlet Ring and Unconditional Bases in $L_2[0,2\pi]$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 3, pp. 75-81. http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a5/

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