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Journal of Mathematical Sciences

, Volume 200, Issue 1, pp 26–45 | Cite as

Spectral Decomposition of Cyclic Operators in Discrete Harmonic Analysis

  • M. S. Bespalov
Article
  • 44 Downloads

Abstract

For the operators of the discrete Fourier transform, the discrete Vilenkin–Christenson transform, and all linear transpositions of the discrete Walsh transform, we obtain their spectral decompositions and calculate the dimensions of eigenspaces. For complex operators, namely, the discrete Fourier transform and the Vilenkin–Christenson transform, we obtain real projectors on eigenspaces. For the discrete Walsh transform, we consider in detail the Paley and Walsh orderings and a new ordering in which the matrices of operators are symmetric. For operators of linear transpositions of the discrete Walsh transforms with nonsymmetric matrices, we obtain a spectral decomposition with complex projectors on eigenspaces. We also present the Parseval frame for eigenspaces of the discrete Walsh transform.

Keywords

Discrete Fourier Transform Digital Signal Processing Cyclic Operator Matrix Versus Spectral Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Vladimir State UniversityVladimirRussia

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