We consider an arbitrary locally compact abelian group $G$,
with an ordered dual group
${\mit \Gamma }$, acting on a space of measures. Under suitable
conditions, we define the notion of analytic measures using the
representation of $G$ and the order on
${\mit \Gamma }$. Our goal is to study analytic measures by
applying a new transference principle for subspaces of measures,
along with results from probability and Littlewood–Paley
theory. As a consequence, we derive new properties of analytic
measures as well as extensions of previous work of Helson and
Lowdenslager, de Leeuw and Glicksberg, and Forelli.
Keywords:
consider arbitrary locally compact abelian group ordered dual group mit gamma acting space measures under suitable conditions define notion analytic measures using representation order mit gamma study analytic measures applying transference principle subspaces measures along results probability littlewood paley theory consequence derive properties analytic measures extensions previous work helson lowdenslager leeuw glicksberg forelli
Affiliations des auteurs :
Nakhlé Asmar
1
;
Stephen Montgomery-Smith
1
1
Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
@article{10_4064_sm146_3_4,
author = {Nakhl\'e Asmar and Stephen Montgomery-Smith},
title = {Decomposition of analytic measures on groups
and measure spaces},
journal = {Studia Mathematica},
pages = {261--284},
year = {2001},
volume = {146},
number = {3},
doi = {10.4064/sm146-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm146-3-4/}
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TY - JOUR
AU - Nakhlé Asmar
AU - Stephen Montgomery-Smith
TI - Decomposition of analytic measures on groups
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Nakhlé Asmar; Stephen Montgomery-Smith. Decomposition of analytic measures on groups
and measure spaces. Studia Mathematica, Tome 146 (2001) no. 3, pp. 261-284. doi: 10.4064/sm146-3-4
