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Uniqueness and quasimeasures on the group of integers of a $ p$-series field


Authors: William R. Wade and Kaoru Yoneda
Journal: Proc. Amer. Math. Soc. 84 (1982), 202-206
MSC: Primary 43A50; Secondary 12B40, 22E50, 42C99
DOI: https://doi.org/10.1090/S0002-9939-1982-0637169-9
Erratum: Proc. Amer. Math. Soc. 88 (1983), 378.
MathSciNet review: 637169
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Abstract: Let $ G$ be the group of integers of a $ p$-series field and suppose that $ S$ is a character series on $ G$. If $ {N_1}$, $ {N_2}, \ldots $ is any sequence of integers and if $ {S_{{p^{{N_j}}}}} \to 0$ a.e. on $ G$, as $ j \to \infty $, then $ S$ will be the zero series provided $ S$ never diverges unboundedly.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0637169-9
Keywords: Group of integers of a $ p$-series field, uniqueness, Walsh functions, Egoroff's Theorem
Article copyright: © Copyright 1982 American Mathematical Society

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