A property of Fourier Stieltjes transforms on the discrete group of real numbers

Domar, Yngve. "A property of Fourier Stieltjes transforms on the discrete group of real numbers." Annales de l'institut Fourier 20.2 (1970): 325-334. <http://eudml.org/doc/74018>.

@article{Domar1970,
abstract = {Let $\mu $ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on $\{\bf R\}$. Then for every $\varepsilon &gt;0$, $\lbrace x\in \{\bf R\}\vert \, \{\rm Re\}\, (\mu (x))&gt;\varepsilon \rbrace $ has a vanishing interior Lebesgue measure. If $\varepsilon =0$ the statement is not generally true. The result is applied to prove a theorem of Rosenthal.},
author = {Domar, Yngve},
journal = {Annales de l'institut Fourier},
keywords = {integral equations, integral transforms},
language = {eng},
number = {2},
pages = {325-334},
publisher = {Association des Annales de l'Institut Fourier},
title = {A property of Fourier Stieltjes transforms on the discrete group of real numbers},
url = {http://eudml.org/doc/74018},
volume = {20},
year = {1970},
}

TY - JOUR
AU - Domar, Yngve
TI - A property of Fourier Stieltjes transforms on the discrete group of real numbers
JO - Annales de l'institut Fourier
PY - 1970
PB - Association des Annales de l'Institut Fourier
VL - 20
IS - 2
SP - 325
EP - 334
AB - Let $\mu $ be a Fourier-Stieltjes transform, defined on the discrete real line and such that the corresponding measure on the dual group vanishes on the set of characters, continuous on ${\bf R}$. Then for every $\varepsilon &gt;0$, $\lbrace x\in {\bf R}\vert \, {\rm Re}\, (\mu (x))&gt;\varepsilon \rbrace $ has a vanishing interior Lebesgue measure. If $\varepsilon =0$ the statement is not generally true. The result is applied to prove a theorem of Rosenthal.
LA - eng
KW - integral equations, integral transforms
UR - http://eudml.org/doc/74018
ER -