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Sbornik: Mathematics, 2016, Volume 207, Issue 8, Pages 1127–1141
DOI: https://doi.org/10.1070/SM8542 (Mi sm8542) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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
English version PDF (478 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM8542
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.
Received: 20.05.2015 and 04.04.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 8, Pages 101–116
DOI: https://doi.org/10.4213/sm8542
Bibliographic databases:
Document Type: Article
UDC: 517.518.8+517.988.8
MSC: 42C15, 42C40
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:68
    First page:35
     
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