Geodesic
Coefficients of convergent multiple Walsh-Paley series
Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1295-1309

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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
Mots-clés : cube convergence, Cantor-Lebesgue theorem. 
@article{SM_2012_203_9_a3,
     author = {M. G. Plotnikov},
     title = {Coefficients of convergent multiple {Walsh-Paley} series},
     journal = {Sbornik. Mathematics},
     pages = {1295--1309},
     publisher = {mathdoc},
     volume = {203},
     number = {9},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_9_a3/}
}
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M. G. Plotnikov. Coefficients of convergent multiple Walsh-Paley series. Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1295-1309. http://geodesic.mathdoc.fr/item/SM_2012_203_9_a3/