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Matematicheskie Zametki, 2014, Volume 96, Issue 4, Pages 483–495
DOI: https://doi.org/10.4213/mzm10309 (Mi mzm10309) 		 
Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity

O. L. Vinogradov

Saint Petersburg State University
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DOI: https://doi.org/10.4213/mzm10309
Abstract: For a certain class of kernels, the exact constant in the estimate of the integral of the product of two functions in terms of the second modulus of continuity of one of them is obtained. Estimates of best approximations by entire functions of exponential type and by splines in terms of the second modulus of continuity of the second derivative of the approximated function are derived from the results obtained. The constants in these estimates are smaller than the previously known ones.
Keywords: estimate of the integral of the product of two functions, best approximation by entire functions, best approximation by splines, second modulus of continuity, Jackson-type inequality.
Received: 23.04.2013
Revised: 09.07.2013
English version:
Mathematical Notes, 2014, Volume 96, Issue 4, Pages 465–476
DOI: https://doi.org/10.1134/S0001434614090211
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: O. L. Vinogradov, “Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity”, Mat. Zametki, 96:4 (2014), 483–495; Math. Notes, 96:4 (2014), 465–476
Citation in format AMSBIB
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