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On certain homomorphisms of restriction algebras of symmetric sets

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Abstract

LetG be a locally compact abelian group and Γ its dual group. For any closedH ⊆G denote the algebra of restrictions toH of Fourier transforms of functions inL 1(Γ) byA(H). This paper considers certain Cantor like sets inR and ΠZ m(j) and gives some necessary algebraic criterion fornatural isomorphisms of their restriction algebras.

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Authors and Affiliations

  1. Stanford University, USA

    Robert Schneider

  2. Cornell University, USA

    Robert Schneider

Authors
  1. Robert Schneider
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Additional information

This work was supported mainly by the U.S. National Science Foundation Graduate Fellowship Program.

The author wishes to thank Paul Cohen, Karel de Leeuw, and Yitzhak Katznelson for their counsel.

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Schneider, R. On certain homomorphisms of restriction algebras of symmetric sets. Israel J. Math. 6, 223–232 (1968). https://doi.org/10.1007/BF02760255

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  • DOI: https://doi.org/10.1007/BF02760255

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