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Mat. Sb., 2016, Volume 207, Number 8, Pages 101–116 (Mi msb8542)  

This article is cited in 1 scientific paper (total in 1 paper)

Calculation of the Riesz constants and orthogonalization for incomplete systems of coherent states by means of theta functions

E. A. Kiselev, L. A. Minin, I. Ya. Novikov

Voronezh State University

Abstract: For systems of coherent states that are multiply rarefied with respect to von Neumann's complete system, we use Jacobi theta functions to obtain exact analytic expressions for the Riesz constants, investigate their behaviour as functions of the ratio of steps in the spatial and frequency domains, construct biorthogonal systems, and realize an orthogonalization procedure that preserves the structure of the windowed Fourier transform.
Bibliography: 19 titles.

Keywords: Riesz systems, coherent states, theta functions, orthogonalization, biorthogonal systems.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8542

Full text: PDF file (512 kB)
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English version:
Sbornik: Mathematics, 2016, 207:8, 1127–1141

Bibliographic databases:

UDC: 517.518.8+517.988.8
MSC: 42C15, 42C40
Received: 20.05.2015 and 04.04.2016

Citation: E. A. Kiselev, L. A. Minin, I. Ya. Novikov, “Calculation of the Riesz constants and orthogonalization for incomplete systems of coherent states by means of theta functions”, Mat. Sb., 207:8 (2016), 101–116; Sb. Math., 207:8 (2016), 1127–1141

Citation in format AMSBIB
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\paper Calculation of the Riesz constants and~orthogonalization for incomplete systems of coherent states by means of theta functions
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\issue 8
\pages 101--116
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\vol 207
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\pages 1127--1141
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  • http://mi.mathnet.ru/eng/msb8542
  • https://doi.org/10.4213/sm8542
  • http://mi.mathnet.ru/eng/msb/v207/i8/p101

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. A. Kiselev, L. A. Minin, I. Ya. Novikov, “Limit Properties of Systems of Integer Translates and Functions Generating Tight Gabor Frames”, Math. Notes, 106:1 (2019), 71–80  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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