We consider an arbitrary locally compact abelian group G, with an ordered dual group Γ, 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 Γ. 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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {147},
year = {2001},
pages = {261-284},
zbl = {0982.43003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-4}
}
Nakhlé Asmar; Stephen Montgomery-Smith. Decomposition of analytic measures on groups and measure spaces. Studia Mathematica, Tome 147 (2001) pp. 261-284. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-4/