## Illinois Journal of Mathematics

### Fourier-Stieltjes transforms with small supports

Colin C. Graham

#### Abstract

Let $G$ be LCA group with dual $\Gamma$. Suppose $S\subseteq \Gamma$ is Borel set such that $S \cap (\gamma-S)$ has finite Haar measure for a dense set of $\gamma \epsilon \Gamma$ (or $S \cap (S-\gamma)$ does). If $\mu$ and $\nu$ are regular Borel measures whose Fourier-Stieltjes transforms vanish off $S$, then $|\mu|\ast|\nu|\epsilon|L^{1}(G)$ ($|\mu|$ denotes the total variation measure). This generalizes to non-metrizable groups a result of Glicksberg. Related results are given; the proofs are elementary.

#### Article information

Source
Illinois J. Math., Volume 18, Issue 4 (1974), 532-534.

Dates
First available in Project Euclid: 20 October 2009

https://projecteuclid.org/euclid.ijm/1256051003

Digital Object Identifier
doi:10.1215/ijm/1256051003

Mathematical Reviews number (MathSciNet)
MR0350324

Zentralblatt MATH identifier
0288.43004

#### Citation

Graham, Colin C. Fourier-Stieltjes transforms with small supports. Illinois J. Math. 18 (1974), no. 4, 532--534. doi:10.1215/ijm/1256051003. https://projecteuclid.org/euclid.ijm/1256051003