A Riesz product proof of the Wiener-Pitt theorem

A Riesz product proof of the Wiener-Pitt theorem
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by Colin C. Graham PDF

Proc. Amer. Math. Soc. 44 (1974), 312-314 Request permission

A Riesz product proof of the Wiener-Pitt theorem is given.

References

I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726
Richard R. Goldberg, Restrictions of Fourier transforms and extension of Fourier sequences, J. Approximation Theory 3 (1970), 149–155. MR 261269, DOI 10.1016/0021-9045(70)90023-7
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups, Die Grundlehren der mathematischen Wissenschaften, Band 152, Springer-Verlag, New York-Berlin, 1970. MR 0262773
Edwin Hewitt and Herbert S. Zuckerman, Singular measures with absolutely continuous convolution squares, Proc. Cambridge Philos. Soc. 62 (1966), 399–420. MR 193435, DOI 10.1017/s0305004100039992
Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
N. Wiener and H. R. Pitt, On absolutely convergent Fourier-Stieltjes transforms, Duke Math. J. 4 (1938), no. 2, 420–436. MR 1546064, DOI 10.1215/S0012-7094-38-00435-1