Geodesic
Sets of Uniqueness for the Group of Integers of a p-Series Field
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 858-866

Voir la notice de l'article provenant de la source Cambridge University Press

Let G denote the group of integers of a p-series field, where p is a prime ≦ 2. Thus, any element can be represented as a sequence {xi }i = 0 ∞ with 0 ≦ xi < p for each i ≦ 0. Moreover, the dual group {Ψm }m = 0 ∞ of G can be described by the following process. If m is a non-negative integer with for each k , and if then (1) where for each integer k ≧ 0 and for each x = {xi } ∈ G the functions Φk are defined by (2) In the case that p = 2, the group G is the dyadic group introduced by Fine [1] and the functions are the Walsh-Paley functions. A detailed account of these groups and basic properties can be found in [4]. 
Wade, William R. Sets of Uniqueness for the Group of Integers of a p-Series Field. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 858-866. doi: 10.4153/CJM-1979-081-7
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[1] 1. Fine, N. J., On the Walsh functions, Trans, A. M. S. 65 (1949), 372–414. Google Scholar

[2] 2. Lindahl, R. J., A differentiation theorem for functions defined on the dyadic rationals, Proc. A. M. S. 30 (1971), 349–352. Google Scholar

[3] 3. Sneider, A., On uniqueness of expansions in Walsh functions, Mat. Sbornik N. S. 24 (1949), 379–400. Google Scholar

[4] 4. Taibleson, M. H., Fourier analysis on local fields (Mathematical Notes, Princeton University Press, Princeton, 1975). Google Scholar

[5] 5. Wade, W. R., Uniqueness and a-capacity on the group 2”, Trans. A. M. S. 208 (1975), 309–315. Google Scholar

[6] 6. Zygmund, A., Trigonometric series (2nd ed. Vol. I, Cambridge University Press, New York, 1959). Google Scholar

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