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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1970, Volume 8, Issue 1, Pages 47–58 (Mi mz9580)

The convergence of trigonometric series to functions of bounded variation

K. I. Oskolkov

Moscow Physicotechnological Institute

Abstract: Necessary and sufficient conditions are derived for the convergence of a trigonometric series to a function of bounded variation on the interval $(\alpha,\beta)\subset[-\pi,\pi]$. For the case in which the coefficients satisfy certain conditions, the continuity of the sum function is investigated.

Full text: PDF file (904 kB)

English version:
Mathematical Notes, 1970, 8:1, 496–503

Bibliographic databases:

UDC: 517.5

Citation: K. I. Oskolkov, “The convergence of trigonometric series to functions of bounded variation”, Mat. Zametki, 8:1 (1970), 47–58; Math. Notes, 8:1 (1970), 496–503

Citation in format AMSBIB
\Bibitem{Osk70} \by K.~I.~Oskolkov \paper The convergence of trigonometric series to functions of bounded variation \jour Mat. Zametki \yr 1970 \vol 8 \issue 1 \pages 47--58 \mathnet{http://mi.mathnet.ru/mz9580} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=279516} \zmath{https://zbmath.org/?q=an:0214.32003} \transl \jour Math. Notes \yr 1970 \vol 8 \issue 1 \pages 496--503 \crossref{https://doi.org/10.1007/BF01093441}