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This article is cited in 7 scientific papers (total in 7 papers)
On rearrangements of conditionally convergent series of functions
P. A. Kornilov
Abstract:
The question of the linearity of the set of sums of the function series $\sum^\infty_{n=1}\varphi_n(x)$ is investigated. It is shown that the requirement $\sum^\infty_{n=1}\|\varphi_n\|^p_{L_p}<\infty$ in the theorem of Kadec ensuring the linearity of the set of sums of a series in the spaces $L_p(0,1)$ with $1\leqslant p\leqslant2$ is definitive. In §2 it is shown that no nontrivial requirement on the norms of the functions of the series or on their absolute values can be sufficient for the linearity of the set of sums of the series in the space $C[a,b]$.
Bibliography: 7 titles.
Received: 31.03.1980
Citation:
P. A. Kornilov, “On rearrangements of conditionally convergent series of functions”, Mat. Sb. (N.S.), 113(155):4(12) (1980), 598–616; Math. USSR-Sb., 41:4 (1982), 495–510
Linking options:
https://www.mathnet.ru/eng/sm2823https://doi.org/10.1070/SM1982v041n04ABEH002244 https://www.mathnet.ru/eng/sm/v155/i4/p598
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Abstract page: | 318 | Russian version PDF: | 114 | English version PDF: | 8 | References: | 34 |
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