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 Mat. Zametki, 2016, Volume 99, Issue 1, Pages 35–41 (Mi mz10689)

Determination of the Jump of a Function of Generalized Bounded Variation from the Derivatives of the Partial Sums of Its Fourier Series

A. A. Kelzon

Admiral Makarov State University of Maritime and Inland Shipping

Abstract: It is established that the formulas determining the jump of a periodic function from the derivatives of the partial sums of its Fourier series and valid for functions of harmonic bounded variation (the HBV class) possibly will not hold for functions of $\Phi$-bounded variation (in the sense of Schramm) if this class is wider than the HBV class.

Keywords: jump of a periodic function, function of harmonic bounded variation, function of $\Phi$-bounded variation, partial sum, Fourier series.

DOI: https://doi.org/10.4213/mzm10689

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English version:
Mathematical Notes, 2016, 99:1, 46–51

Bibliographic databases:

UDC: 517.518
Revised: 20.06.2015

Citation: A. A. Kelzon, “Determination of the Jump of a Function of Generalized Bounded Variation from the Derivatives of the Partial Sums of Its Fourier Series”, Mat. Zametki, 99:1 (2016), 35–41; Math. Notes, 99:1 (2016), 46–51

Citation in format AMSBIB
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