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- W2008522864 abstract "Suppose T is a bounded self-adjoint operator on the Hilbert space L2(X,μ) and letT=∫SpL2TλdE(λ) be its spectral resolution. Let F be a Borel bounded function on [−a,a], SpL2T⊂[−a,a]. We say that F is a spectral Lp-multiplier for T, ifF(T)=∫SpL2TF(λ)dE(λ) is a bounded operator on Lp(X,μ). The paper deals with l1-multipliers, where X=G is a discrete (countable) solvable group with ∀x∈G, x4=1, μ is the counting measure andTΦ:l2(G)∋ξ↦ξ∗Φ∈l2(G), where Φ=Φ∗ is a l1(G) function, suppΦ generates G. The main result of the paper states that there exists a Ψ on G such that all l1-multipliers for TΨ are real analytic at every interior point of Spl2(G)TΨ. We also exhibit self-adjoint Φ′s in l1(G) such that suppΦ generates G and F∈Cc2 are l1-multipliers for TΦ." @default.
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- W2008522864 date "2009-02-01" @default.
- W2008522864 modified "2023-09-24" @default.
- W2008522864 title "Functional calculi for convolution operators on a discrete, periodic, solvable group" @default.
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- W2008522864 doi "https://doi.org/10.1016/j.jfa.2008.11.011" @default.
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