Coefficients of convergent multiple Walsh-Paley series

M. G. Plotnikov

Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1295-1309

Résumé

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.

Détail

Keywords: multiple Walsh-Paley series
Mots-clés : cube convergence, Cantor-Lebesgue theorem.

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