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Additional information
The content of § 2 and part of Theorem 2 appeared in my thesis. I wish to thank ProfessorLynn Loomis most cordially for his direction. The other parts have roots in conversations with ProfessorArne Beurling.
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Helson, H. Spectral synthesis of bounded functions. Ark. Mat. 1, 497–502 (1952). https://doi.org/10.1007/BF02591359
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DOI: https://doi.org/10.1007/BF02591359