Restrictions of Fourier transforms of continuous measures
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- by Benjamin B. Wells PDF
- Proc. Amer. Math. Soc. 38 (1973), 92-94 Request permission
Abstract:
Let $G$ denote a compact abelian group and $\Gamma$ its discrete dual. It is proved that $E \subset \Gamma$ is Sidon if and only if the restriction to $E$ of the algebra of Fourier transforms of continuous measures on $G$ is all of ${l_\infty }(E)$.References
- Stephen William Drury, Sur les ensembles de Sidon, C. R. Acad. Sci. Paris Sér. A-B 271 (1970), A162–A163 (French). MR 271647
- W. F. Eberlein, The point spectrum of weakly almost periodic functions, Michigan Math. J. 3 (1955/56), 137–139. MR 82627
- I. Glicksberg and I. Wik, The range of Fourier-Stieltjes transforms of parts of measures, Conference on Harmonic Analysis (Univ. Maryland, College Park, Md., 1971), Lecture Notes in Math., Vol. 266, Springer, Berlin, 1972, pp. 73–77. MR 0433145
- 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
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 92-94
- MSC: Primary 43A46; Secondary 43A25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0315364-0
- MathSciNet review: 0315364