Article contents
The spectral mapping property for p–multiplier operators on compact abelian groups
Published online by Cambridge University Press: 09 April 2009
Abstract
Let G be a compact abelian group and 1< p < ∞. It is known that the spectrum σ (Tψ) of a Fourier p–multiplier operator Tψ acting in Lp(G), may fail to coincide with its natural spectrum ψ(Г) if p ≠ 2; here Γ is the dual group to G and the bar denotes closure in C. Criteria are presented, based on geometric, topological and/or algebraic properties of the compact set σ(Tψ), which are sufficient to ensure that the equality σ(Tψ) = ψ(Г)holds.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 2005
References
- 2
- Cited by