ISSN:
1436-5081
Keywords:
22B05
;
43A15
;
Compact Abelian group
;
group generators
;
n-thetic groups
;
differences
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetG be a Hausdorff compact Abelian group andC be the component of the identity element ofG. We consider a special class, ℋ(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 ℋ(G), there area 1,...,a n inG and functionf 1,...f n in ℋ(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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01326034
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