Book chapter
Approximation Theory on the Compact Solenoid
Functional Analysis and Approximation, pp.167-174
Birkhäuser Basel
1981
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.
Details
- Title
- Approximation Theory on the Compact Solenoid
- Authors/Creators
- W.R. Bloom (Author/Creator)
- Contributors
- P.L. Butzer (Editor)B. Sz.-Nagy (Editor)E. Görlich (Editor)
- Publication Details
- Functional Analysis and Approximation, pp.167-174
- Publisher
- Birkhäuser Basel
- Identifiers
- 991005542760807891
- Copyright
- 1981 Birkhäuser Verlag Basel
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Book chapter
- Additional Information
- Series Title ISNM 60: International Series of Numerical Mathematics
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