Decomposition of analytic measures on groups and measure spaces

Nakhlé Asmar, and Stephen Montgomery-Smith. "Decomposition of analytic measures on groups and measure spaces." Studia Mathematica 146.3 (2001): 261-284. <http://eudml.org/doc/284657>.

@article{NakhléAsmar2001,
abstract = {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.},
author = {Nakhlé Asmar, Stephen Montgomery-Smith},
journal = {Studia Mathematica},
keywords = {measure spaces; sup path attaining; F. and M. Riesz theorem; locally compact abelian group},
language = {eng},
number = {3},
pages = {261-284},
title = {Decomposition of analytic measures on groups and measure spaces},
url = {http://eudml.org/doc/284657},
volume = {146},
year = {2001},
}

TY - JOUR
AU - Nakhlé Asmar
AU - Stephen Montgomery-Smith
TI - Decomposition of analytic measures on groups and measure spaces
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 3
SP - 261
EP - 284
AB - 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.
LA - eng
KW - measure spaces; sup path attaining; F. and M. Riesz theorem; locally compact abelian group
UR - http://eudml.org/doc/284657
ER -