Differences of functions and groups generators for compact Abelian groups |
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Authors: | Wai Lok Lo Rodney Nillsen |
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Institution: | 1. Mathematics Department, University of Wollongong, Northfields Avenue, 2522, Wollongong, New South Wales, Australia
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Abstract: | LetG be a Hausdorff compact Abelian group andC be the component of the identity element ofG. We consider a special class, ?(G), of functions inL 2 (G) whose Fourier series satisfy certain convergence conditions (stronger than absolute convergence). We show thatG/C is topologically generated by not more thann elements if and only if, for each functionf in ?(G), there area 1,...,a n inG and functionf 1,...f n in ?(G) such that $$f = \sum\limits_{j = 1}^n {(f_j - \delta _{aj} * f_j ),}$$ where * is convolution defined in the usual sense, and δ a denotes the Dirac measure ataεG. |
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