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Mat. Sb., 2012, Volume 203, Number 9, Pages 67–82 (Mi msb7859)  

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.

DOI: https://doi.org/10.4213/sm7859

Full text: PDF file (548 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2012, 203:9, 1295–1309

Bibliographic databases:

UDC: 517.518
MSC: 42C10, 42B05
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

Citation in format AMSBIB
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  • Математический сборник Sbornik: Mathematics (from 1967)
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