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

Annales de l'institut Fourier (1970)

- Volume: 20, Issue: 2, page 325-334
- ISSN: 0373-0956

## Access Full Article

top## Abstract

top## How to cite

topDomar, 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 $\varepsilon >0$, $\lbrace x\in \{\bf R\}\vert \, \{\rm Re\}\, (\mu (x))>\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 $\varepsilon >0$, $\lbrace x\in {\bf R}\vert \, {\rm Re}\, (\mu (x))>\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 -

## References

top- [1] H. ROSENTHAL, A characterization of restrictions of Fourier-Stieltjes transforms, Pac. J. Math. 23 (1967) 403-418. Zbl0155.18901MR36 #3065
- [2] W. RUDIN, Fourier analysis on groups. New York 1962. Zbl0107.09603MR27 #2808

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.