Abstract
In this paper we generalize the classical Bernstein theorem concerning the absolute convergence of the Fourier series of Lipschitz functions. More precisely, we consider a group G which is finite dimensional, compact, and separable and has an infinite, closed, totally disconnected, normal subgroup D, such that G D is a Lie group. Using this structure, we define in a natural way the notion of Lipschitz condition, and then prove that a function which satisfies a Lipschitz condition of order greater than ( dim G + 1) 2 belongs to the Fourier algebra of G.
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