Functions which are Fourier-Stieltjes transforms
HTML articles powered by AMS MathViewer
- by Stephen H. Friedberg PDF
- Proc. Amer. Math. Soc. 28 (1971), 451-452 Request permission
Abstract:
Let $G$ be a locally compact abelian group, $\hat G$ the dual group, $M(G)$ the algebra of regular bounded Borel measures on $G$, and $M{(G)^\wedge }$ the algebra of Fourier-Stieltjes transforms. The purpose of this paper is to characterize those continuous functions on $\hat G$ which belongs to $M(X)^\wedge$, where $X$ is a closed subset of $G$ and $M(X) = \{ \mu \in M(G)$: the support of $\mu$ is contained in $X\}$.References
- Gottfried Köthe, Topologische lineare Räume. I, Die Grundlehren der mathematischen Wissenschaften, Band 107, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). MR 0130551
- Donald E. Ramirez, Uniform approximation by Fourier-Stieltjes transforms, Proc. Cambridge Philos. Soc. 64 (1968), 323–333. MR 221221, DOI 10.1017/s0305004100042882
- 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 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 451-452
- MSC: Primary 42.52
- DOI: https://doi.org/10.1090/S0002-9939-1971-0278006-7
- MathSciNet review: 0278006