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On a characterization of Fourier transforms. (English) Zbl 0146.12103

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[1] H. Cramér, ?On the representations of a function by certain Fourier integrals?, Trans. Amer. Math. Soc.46 (1939), pp. 191-201.
[2] W. Rudin, Fourier analysis on groups, Interscience Publishers, New York, 1962. · Zbl 0107.09603
[3] E. Hewitt, ?A new proof of Plancherel’s theorem for locally compact Abelian groups?, Acta Sci. Math. Szeged24 (1963), pp. 219-227. · Zbl 0168.11503
[4] I. J. Schoenberg, ?A remark on the preceding note by Bochner?, Bull. Amer. Math. Soc.40 (1934), pp. 277-278. · Zbl 0009.24704
[5] W. F. Eberlein, ?Characterization of Fourier-Stieltjes transforms?, Duke Math. J.22 (1955), pp. 465-468. · Zbl 0065.01603
[6] R. Ryan, ?Fourier transforms of certain classes of integrable functions?, Trans. Amer. Math. Soc.105 (1962), pp. 102-111. · Zbl 0107.09701
[7] R. Salem, ?Les coefficients de Fourier des functions sommables?, C. R. Acad. Sci., Paris192 (1931), pp. 144-146. · JFM 57.0316.01
[8] A. C. Berry, ?Necessary and sufficient conditions in the theory of Fourier transforms?, Ann. of Math.32 (1931), pp. 830-838. · JFM 57.0482.02
[9] E. Hewitt andK. R. Stromberg, ?A remark on Fourier-Stieltjes transforms?, Annals. Acad. Brasil, Ci.34 (1962), pp. 175-180. · Zbl 0117.09601
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