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Matematicheskie Zametki, 2016, Volume 100, Issue 3, Pages 323–330
DOI: https://doi.org/10.4213/mzm11014 (Mi mzm11014) 		 
On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials

P. A. Andrianov, O. L. Vinogradov

Saint Petersburg State University
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DOI: https://doi.org/10.4213/mzm11014
Abstract: Two sharp results for best approximations of periodic functions are established in this paper. We prove the sharpness of the step of the modulus of continuity in Jackson's inequality with least possible constant for approximations by trigonometric polynomials. We also prove the sharpness of the constants in a Jackson-type inequality for approximations by Haar polynomials in several variables.
Keywords: sharp constant, Jackson's inequality, Haar system.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-05796-а
Saint Petersburg State University 9.38.198.2015
The work of the first author was supported by the Russian Foundation for Basic Research under grant 15-01-05796-a and by St. Petersburg State University (research grant no. 9.38.198.2015).
Received: 09.11.2015
Revised: 30.01.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 3, Pages 345–351
DOI: https://doi.org/10.1134/S0001434616090017
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: P. A. Andrianov, O. L. Vinogradov, “On the Constant and Step in Jackson's Inequality for Best Approximations by Trigonometric Polynomials and by Haar Polynomials”, Mat. Zametki, 100:3 (2016), 323–330; Math. Notes, 100:3 (2016), 345–351
Citation in format AMSBIB
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