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- W3145809621 abstract "where a (x) is a character and the sum is over all the characters. This paper begins a s tudy of the Abel summabil i ty of this series and developes the theory for countable toral groups. Let G be a countable toral group. Let X C~ be a decomposition of G into an infinite direct product, where each C~ is the group of reals modulo one. The topology and measure of G are the product topology and measure. The characters of G will be isomorphic to the direct product of countably many infinite cyclic groups. Let a = {an} be a sequence of integral multiples of 2 rc with only a finite number of them different from zero. The collection of all a 's is isomorphic to G with addition defined termwise. A point in G is a sequence x = (xn} and each a(x) = exp [-i Xa,,xn]. By the Abel sum of the Fourier series (1) we shall mean: (2) lira • r~l~l/2~ f/(x) ff(y x ) d x . r--~l a" @default.
- W3145809621 created "2021-04-13" @default.
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- W3145809621 date "2005-01-01" @default.
- W3145809621 modified "2023-09-26" @default.
- W3145809621 title "A Summability Theorem in Countable Toral Groups" @default.
- W3145809621 hasPublicationYear "2005" @default.
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