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This article is cited in 1 scientific paper (total in 1 paper)
Coefficients of convergent multiple Walsh-Paley series
M. G. Plotnikov Vologda State Academy of Milk Industry
Abstract:
The paper is concerned with the behaviour of the coefficients of multiple Walsh-Paley series that are cube convergent to a finite sum. It is shown that even an everywhere convergent series of this kind may contain coefficients with numbers from a sufficiently large set that grow faster than any preassigned sequence. By Cohen's theorem, this sort of thing cannot happen for multiple trigonometric series that are cube convergent on a set of full measure — their coefficients cannot grow even exponentially. Null subsequences of coefficients are determined for multiple Walsh-Paley series that are cube convergent on a set of definite measure.
Bibliography: 18 titles.
Keywords:
multiple Walsh-Paley series, cube convergence, Cantor-Lebesgue theorem.
Received: 02.03.2011 and 19.04.2012
Citation:
M. G. Plotnikov, “Coefficients of convergent multiple Walsh-Paley series”, Mat. Sb., 203:9 (2012), 67–82; Sb. Math., 203:9 (2012), 1295–1309
Linking options:
https://www.mathnet.ru/eng/sm7859https://doi.org/10.1070/SM2012v203n09ABEH004265 https://www.mathnet.ru/eng/sm/v203/i9/p67
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Abstract page: | 593 | Russian version PDF: | 192 | English version PDF: | 12 | References: | 64 | First page: | 33 |
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