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Approximation Theory on the Compact Solenoid
Book chapter

Approximation Theory on the Compact Solenoid

W.R. Bloom
Functional Analysis and Approximation, pp.167-174
Birkhäuser Basel
1981
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Abstract

The compact solenoid Σ is the a-adic solenoid with a = (2,3,…). It is a compact connected metrisable abelian group with dual the group of rational numbers. We give an analogue of the M. Riesz theorem on the boundedness of partial sums of the Fourier series of functions in LP(Σ), and use this to characterize the Lipschitz functions on Σ in terms of the rate of convergence of their Fourier series. In addition we prove a factorization theorem for these functions.

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