Abstract
We study increasing sequences of positive integers that divide the Fourier series of functions of bounded variation into blocks of absolutely convergent series. We obtain a new version of the stability theorem for such sequences.
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S. A. Telyakovskii, “On Partial Sums of Fourier Series of Functions of Bounded Variation,” Trudy MIAN 219, 378–386(1997).
A. S. Belov and S. A. Telyakovskii, ”Refinement of the Dirichlet-Jordan and Young’s Theorems on Fourier Series of Functions of Bounded Variation,” Matem. Sborn. 198(6), 25–40 (2007).
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Original Russian Text © S. A. Telyakovskii, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 3, pp. 48–51
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Telyakovskii, S.A. The nature of convergence of the Fourier series for functions of bounded variation. Russ Math. 54, 42–44 (2010). https://doi.org/10.3103/S1066369X10030072
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DOI: https://doi.org/10.3103/S1066369X10030072