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Matematicheskie Zametki, 2002, Volume 71, Issue 2, Pages 239–253
DOI: https://doi.org/10.4213/mzm343 (Mi mzm343) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Asymptotics of the Roots of Bernstein Polynomials Used in the Construction of Modified Daubechies Wavelets

I. Ya. Novikov

Voronezh State University
Full-text PDF (262 kB) Citations (20)
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DOI: https://doi.org/10.4213/mzm343
Abstract: This paper is devoted to the study of the asymptotics of roots of a sequence of Bernstein polynomials approximating a piecewise linear function. This sequence arises in the construction of modified compactly supported wavelets that, in contrast to classical Daubechies wavelets, preserve localization with the growth of smoothness. It is proved that the limiting curve for roots is the boundary of the domain of convergence of the Bernstein polynomials on the complex plane.
Received: 08.06.2000
English version:
Mathematical Notes, 2002, Volume 71, Issue 2, Pages 217–229
DOI: https://doi.org/10.1023/A:1013959231555
Bibliographic databases:
UDC: 517.518.865
Language: Russian
Citation: I. Ya. Novikov, “Asymptotics of the Roots of Bernstein Polynomials Used in the Construction of Modified Daubechies Wavelets”, Mat. Zametki, 71:2 (2002), 239–253; Math. Notes, 71:2 (2002), 217–229
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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