Document Zbl 0394.43005

Balayage by Fourier transforms with sparse frequencies in compact Abelian torsion groups. (English) Zbl 0394.43005

Proc. Am. Math. Soc. 71, 253-256 (1978).

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MSC:

43A25	Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
42A55	Lacunary series of trigonometric and other functions; Riesz products
43A70	Analysis on specific locally compact and other abelian groups

Keywords:

Fourier Transforms with Sparse Frequencies; Compact Abelian Torsion Groups; Balayage

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References:

[1]	A. Beurling, On balayage of measures in Fourier transforms, Notes from a seminar at the Institute for Advanced Study, Princeton, N. J., 1959-60 (unpublished).
[2]	E. Hewitt and K. A. Ross, Abstract harmonic analysis. I, Grundlehren Math. Wiss., Band 115, Springer-Verlag, Berlin and New York, 1963. · Zbl 0115.10603
[3]	Jean-Pierre Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin-New York, 1970 (French). · Zbl 0195.07602
[4]	Jean-Pierre Kahane and Raphaël Salem, Ensembles parfaits et séries trigonométriques, Actualités Sci. Indust., No. 1301, Hermann, Paris, 1963 (French). · Zbl 0112.29304
[5]	George S. Shapiro, Balayage in Fourier transforms: general results, perturbation, and balayage with sparse frequencies, Trans. Amer. Math. Soc. 225 (1977), 183 – 198. · Zbl 0343.43002

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