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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Uniqueness and $ \alpha $-capacity on the group $ 2\sp{\omega }$


Author: William R. Wade
Journal: Trans. Amer. Math. Soc. 208 (1975), 309-315
MSC: Primary 42A62
DOI: https://doi.org/10.1090/S0002-9947-1975-0380255-2
MathSciNet review: 0380255
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Abstract: We introduce a class of Walsh series $ \mathcal{J}_\alpha ^ + $ for each $ 0 < \alpha < 1$ and show that a necessary and sufficient condition that a closed set $ E \subseteq {2^\omega }$ be a set of uniqueness for $ \mathcal{J}_\alpha ^ + $ is that the $ \alpha $-capacity of $ E$ be zero.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0380255-2
Keywords: Haar functions, Walsh functions, sets of uniqueness, $ \alpha $-capacity
Article copyright: © Copyright 1975 American Mathematical Society

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