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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     author = {A. Sowa},
     title = {The {Dirichlet} {Ring} and {Unconditional} {Bases} in $L_2[0,2\pi]$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {75--81},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_3_a5/}
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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/