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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 3, Pages 75–81 (Mi faa3113)  

This article is cited in 4 scientific papers (total in 4 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.

DOI: https://doi.org/10.4213/faa3113

Full text: PDF file (145 kB)
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English version:
Functional Analysis and Its Applications, 2013, 47:3, 227–232

Bibliographic databases:

UDC: 517.98
Received: 06.06.2011

Citation: A. Sowa, “The Dirichlet Ring and Unconditional Bases in $L_2[0,2\pi]$”, Funktsional. Anal. i Prilozhen., 47:3 (2013), 75–81; Funct. Anal. Appl., 47:3 (2013), 227–232

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Sowa, “Riemann's zeta function and the broadband structure of pure harmonics”, IMA J. Appl. Math., 82:6 (2017), 1238–1252  crossref  mathscinet  isi  scopus
    2. A. Sowa, “Image processing via simulated quantum dynamics”, Random Oper. Stoch. Equ., 25:1 (2017), 27–39  crossref  mathscinet  zmath  isi  scopus
    3. Sowa A., “A Nonlocal Transform to Map and Track Quantum Dynamics”, J. Phys. A-Math. Theor., 52:30 (2019), 305301  crossref  isi
    4. E. V. Burlachenko, “The Riordan–Dirichlet Group”, Math. Notes, 106:4 (2019), 514–525  mathnet  crossref  crossref  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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