Idele characters in spectral synthesis on $𝐑/2\pi 𝐙$

Benedetto, John J.. "Idele characters in spectral synthesis on ${\bf R}/2\pi {\bf Z}$." Annales de l'institut Fourier 23.4 (1973): 45-64. <http://eudml.org/doc/74153>.

@article{Benedetto1973,
abstract = {Let $s\in \{\bf C\}$, $x\in \{\bf R\}/2\pi \{\bf Z\}$. We construct Dirichlet series $F(x,x)$ where for each fixed $s$ in a half plane, $\{\rm Re\}\, F(x,x)$, as a function of $x$, is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in $F$ are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when $\{\rm Re\}\, s\le 1$.},
author = {Benedetto, John J.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {45-64},
publisher = {Association des Annales de l'Institut Fourier},
title = {Idele characters in spectral synthesis on $\{\bf R\}/2\pi \{\bf Z\}$},
url = {http://eudml.org/doc/74153},
volume = {23},
year = {1973},
}

TY - JOUR
AU - Benedetto, John J.
TI - Idele characters in spectral synthesis on ${\bf R}/2\pi {\bf Z}$
JO - Annales de l'institut Fourier
PY - 1973
PB - Association des Annales de l'Institut Fourier
VL - 23
IS - 4
SP - 45
EP - 64
AB - Let $s\in {\bf C}$, $x\in {\bf R}/2\pi {\bf Z}$. We construct Dirichlet series $F(x,x)$ where for each fixed $s$ in a half plane, ${\rm Re}\, F(x,x)$, as a function of $x$, is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in $F$ are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when ${\rm Re}\, s\le 1$.
LA - eng
UR - http://eudml.org/doc/74153
ER -