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This article is cited in 1 scientific paper (total in 1 paper)
Limits of indeterminacy in measure of $T$-means of trigonometric series
D. E. Men'shov
Abstract:
The following theorem is proved. Let $F(x)$ and $G(x)$ be arbitrary measurable functions such that $G(x)\leqslant F(x)$ almost everywhere on $[-\pi,\pi]$, and let $T$ be an arbitrary row-finite summation method defined by a real matrix. Then there exists a trigonometric series whose coefficients tend to zero and such that the limits of indeterminacy of its $T$-means are exactly $F(x)$ and $G(x)$.
Bibliography: 8 titles.
Received: 08.12.1969
Citation:
D. E. Men'shov, “Limits of indeterminacy in measure of $T$-means of trigonometric series”, Math. USSR-Sb., 10:4 (1970), 441–474
Linking options:
https://www.mathnet.ru/eng/sm3383https://doi.org/10.1070/SM1970v010n04ABEH001678 https://www.mathnet.ru/eng/sm/v123/i4/p485
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Abstract page: | 530 | Russian version PDF: | 99 | English version PDF: | 14 | References: | 82 |
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