Spectra of convolution operators on Lp spaces
AUTOR(ES)
Zafran, Misha
RESUMO
Let 1 < p < ∞ with p ≠ 2. Let G denote the n-torus or Euclidean n-space, and let Γ be the dual group of G. We show the existence of a multiplier transformation T on Lp(G) which satisfies the following properties: (a) the transform T̂ of T is smooth and vanishes at infinity on Γ; (b) the spectrum of T on Lp properly contains T̂(Γ)∪{0}.
