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 Mat. Zametki, 2014, Volume 96, Issue 4, Pages 483–495 (Mi mz10309)

Sharp Estimates of Integrals in Terms of the Second Modulus of Continuity

Saint Petersburg State University

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.

DOI: https://doi.org/10.4213/mzm10309

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English version:
Mathematical Notes, 2014, 96:4, 465–476

Bibliographic databases:

UDC: 517.5
Revised: 09.07.2013

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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