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Dedicated to Arne Beurling in respectful affection.
The results which are presented here come from a joint work with A. Beurling and were exposed in this form at the Stanford conference in 1961. A more concise proof of the Main Theorem was published in Acta Math. 1962 (107), p. 291–309. This paper will be denoted [A. M.]. It is also referred to [A. M.] for a bibliography.
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Malliavin, P. On the multiplier theorem for Fourier transforms of measures with compact support. Ark. Mat. 17, 69–81 (1979). https://doi.org/10.1007/BF02385458
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DOI: https://doi.org/10.1007/BF02385458