On Uniqueness Properties of Rademacher Chaos Series

For a given integer , let be an arbitrary numeration of the integers permitting a dyadic decomposition with . We prove that (i) the convergence of a Walsh series on a set of measure implies and (ii) if it converges to zero on a set of the same measure , then for all .

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Bibliographische Detailangaben
Veröffentlicht in:	Mathematical Notes 2023-12, Vol.114 (5-6), p.1225-1232
Hauptverfasser:	Karagulyan, G. A., Karagulyan, V. G.
Format:	Artikel
Sprache:	eng
Schlagworte:	14/34 639/766/189 639/766/530 639/766/747 Convergence Mathematics Mathematics and Statistics Series (mathematics)
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	For a given integer , let be an arbitrary numeration of the integers permitting a dyadic decomposition with . We prove that (i) the convergence of a Walsh series on a set of measure implies and (ii) if it converges to zero on a set of the same measure , then for all .
ISSN:	0001-4346 1067-9073 1573-8876
DOI:	10.1134/S0001434623110548