Uniqueness and 𝛼-capacity on the group 2^{𝜔}

Wade, William R.

doi:10.1090/S0002-9947-1975-0380255-2

Uniqueness and $\alpha$-capacity on the group $2^{\omega }$
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Trans. Amer. Math. Soc. 208 (1975), 309-315 Request permission

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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