The spectral mapping property for <i>p</i>–multiplier operators on compact abelian groups

Abstract

Abstract Let G be a compact abelian group and 1&lt; p &lt; ∞. It is known that the spectrum σ (T ψ ) of a Fourier p –multiplier operator Tψ acting in L p (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.

Locations

• Journal of the Australian Mathematical Society - View - PDF