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Approximation Theory on the Compact Solenoid

Bloom, W.R. (1981) Approximation Theory on the Compact Solenoid. In: Butzer, P.L., Sz.-Nagy, B. and Görlich, E., (eds.) Functional Analysis and Approximation. Birkhäuser Basel, pp. 167-174.

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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.

Publication Type: Book Chapter
Murdoch Affiliation: School of Mathematical and Physical Sciences
Publisher: Birkhäuser Basel
Copyright: 1981 Birkhäuser Verlag Basel
Other Information: Series Title ISNM 60: International Series of Numerical Mathematics
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