When is a riesz distribution a complex measure?

Alan D. Sokal

doi:10.24033/bsmf.2617

When is a riesz distribution a complex measure?

Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

Let R_α be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by α ∈ ℂ. I give an elementary proof of the necessary and sufficient condition for R_α to be a locally finite complex measure (= complex Radon measure).

Original language	English (US)
Pages (from-to)	519-534
Number of pages	16
Journal	Bulletin de la Societe Mathematique de France
Volume	139
Issue number	4
DOIs	https://doi.org/10.24033/bsmf.2617
State	Published - 2011

Keywords

Gindikin's theorem
Jordan algebra
Laplace transform
Positive measure
Radon measure
Relatively invariant measure
Riesz distribution
Symmetric cone
Tempered distribution
Wallach set

ASJC Scopus subject areas

General Mathematics

Access to Document

10.24033/bsmf.2617

Cite this

@article{bbf2906c24c643f8a40d39114daa8c24,

title = "When is a riesz distribution a complex measure?",

abstract = "Let Rα be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by α ∈ ℂ. I give an elementary proof of the necessary and sufficient condition for Rα to be a locally finite complex measure (= complex Radon measure).",

keywords = "Gindikin's theorem, Jordan algebra, Laplace transform, Positive measure, Radon measure, Relatively invariant measure, Riesz distribution, Symmetric cone, Tempered distribution, Wallach set",

author = "Sokal, {Alan D.}",

year = "2011",

doi = "10.24033/bsmf.2617",

language = "English (US)",

volume = "139",

pages = "519--534",

journal = "Bulletin de la Societe Mathematique de France",

issn = "0037-9484",