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Mat. Zametki, 2008, Volume 84, Issue 5, Pages 732–740 (Mi mz4002)  

This article is cited in 5 scientific papers (total in 5 papers)

Meyer Wavelets with Least Uncertainty Constant

E. A. Lebedevaa, V. Yu. Protasovb

a Kursk State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In the present paper, we construct a system of Meyer wavelets with least possible uncertainty constant. The uncertainty constant minimization problem is reduced to a convex variational problem whose solution satisfies a second-order nonlinear differential equation. Solving this equation numerically, we obtain the desired system of wavelets.

Keywords: Meyer wavelet, uncertainty constant, variational problem, second-order nonlinear differential equation, Sobolev space, Fourier transform

DOI: https://doi.org/10.4213/mzm4002

Full text: PDF file (538 kB)
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English version:
Mathematical Notes, 2008, 84:5, 680–687

Bibliographic databases:

UDC: 517.518.36+517.972.9
Received: 28.08.2007

Citation: E. A. Lebedeva, V. Yu. Protasov, “Meyer Wavelets with Least Uncertainty Constant”, Mat. Zametki, 84:5 (2008), 732–740; Math. Notes, 84:5 (2008), 680–687

Citation in format AMSBIB
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\paper Meyer Wavelets with Least Uncertainty Constant
\jour Mat. Zametki
\yr 2008
\vol 84
\issue 5
\pages 732--740
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\crossref{https://doi.org/10.4213/mzm4002}
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\transl
\jour Math. Notes
\yr 2008
\vol 84
\issue 5
\pages 680--687
\crossref{https://doi.org/10.1134/S0001434608110096}
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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. Abdollahi A., Cheshmavar J., Taghavi M., “Wavelets generated by the Rudin-Shapiro polynomials”, Cent. Eur. J. Math., 9:2 (2011), 441–448  crossref  mathscinet  zmath  isi  elib  scopus
    2. E. A. Lebedeva, “On the uncertainty principle for Meyer wavelets”, J. Math. Sci. (N. Y.), 182:5 (2012), 656–662  mathnet  crossref
    3. Frunt J., Kling W.L., Ribeiro P.F., “Wavelet Decomposition for Power Balancing Analysis”, IEEE Trans. Power Deliv., 26:3 (2011), 1608–1614  crossref  isi  elib  scopus
    4. Lebedeva E.A., Prestin J., “Periodic Wavelet Frames and Time Frequency Localization”, Appl. Comput. Harmon. Anal., 37:2 (2014), 347–359  crossref  mathscinet  zmath  isi  scopus
    5. Iglewska-Nowak I., “Uncertainty Product of the Spherical Gauss-Weierstrass Wavelet”, Int. J. Wavelets Multiresolut. Inf. Process., 16:4 (2018), 1850030  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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