• Corpus ID: 238856849

Extension of functions on finite sets to Fourier transforms

@inproceedings{Lebedev2021ExtensionOF,
  title={Extension of functions on finite sets to Fourier transforms},
  author={Vladimir Lebedev},
  year={2021}
}
Let Γ be an LCA group and A(Γ) the corresponding Fourier algebra. We show that if K ⊆ Γ is an n-point set, then √ n/2 ≤ αΓ(K) ≤ √ n where αΓ(K) is the infimum of the norms of all linear extension operators from C0(K) to A(Γ). The lower bound implies that if K is an infinite closed subset of Γ, then there does not exist a bounded linear extension operator from C0(K) to A(Γ). 

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