A characterization of Lipschitz classes on finite dimensional groups

An analogue of a theorem of S. N. Bernstein is developed for certain metric locally compact abelian groups. This, together with a corresponding Jackson-type theorem, gives a characterisation in terms of their Fourier transforms of the Lipschitz functions defined on a compact abelian group with finit...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1976-09, Vol.59 (2), p.297-304
Main Author: Bloom, Walter R.
Format: Article
Language:English
Subjects:
Mathematical functions
Mathematical inequalities
Mathematical theorems
Real lines
Research article
Topological dimensions
Topological theorems
Topology
Zero
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Summary:An analogue of a theorem of S. N. Bernstein is developed for certain metric locally compact abelian groups. This, together with a corresponding Jackson-type theorem, gives a characterisation in terms of their Fourier transforms of the Lipschitz functions defined on a compact abelian group with finite topological dimension.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1976-0417654-2