Sets of uniqueness in compact, 0-dimensional metric groups

Grubb, D. J.

doi:10.1090/S0002-9947-1987-0879571-5

Sets of uniqueness in compact, $0$-dimensional metric groups

Author: D. J. Grubb
Journal: Trans. Amer. Math. Soc. 301 (1987), 239-249
MSC: Primary 42C10; Secondary 43A46
DOI: https://doi.org/10.1090/S0002-9947-1987-0879571-5
MathSciNet review: 879571
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Abstract: An investigation is made of sets of uniqueness in a compact $0$-dimensional space. Such sets are defined by pointwise convergence of sequences of functions that generalize partial sums of trigonometric series on Vilenkin groups. Several analogs of classical uniqueness theorems are proved, including a version of N. Bary’s theorem on countable unions of closed sets of uniqueness.

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