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Sbornik: Mathematics, 2005, Volume 196, Issue 3, Pages 395–422
DOI: https://doi.org/10.1070/SM2005v196n03ABEH000885 (Mi sm1277) 		 
Characterization of the best polynomial approximation with a sign-sensitive weight to a continuous function

A.-R. K. Ramazanov

Daghestan State University
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DOI: https://doi.org/10.1070/SM2005v196n03ABEH000885
Abstract: Necessary and sufficient conditions for the best polynomial approximation with an arbitrary and, generally speaking, unbounded sign-sensitive weight to a continuous function are obtained; the components of the weight can also take infinite values, therefore the conditions obtained cover, in particular, approximation with interpolation at fixed points and one-sided approximation; in the case of the weight with components equal to 1 one arrives at Chebyshev's classical alternation theorem.
Received: 29.06.2003 and 12.04.2004
Russian version:
Matematicheskii Sbornik, 2005, Volume 196, Number 3, Pages 89–118
DOI: https://doi.org/10.4213/sm1277
Bibliographic databases:
UDC: 517.5
MSC: Primary 41A10, 41A29; Secondary 41A65
Language: English
Original paper language: Russian
Citation: A. K. Ramazanov, “Characterization of the best polynomial approximation with a sign-sensitive weight to a continuous function”, Mat. Sb., 196:3 (2005), 89–118; Sb. Math., 196:3 (2005), 395–422
Citation in format AMSBIB
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    Russian version PDF:212
    English version PDF:9
    References:72
    First page:1
     
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