When is a Riesz distribution a complex measure?

Alan D. Sokal

Bulletin de la Société Mathématique de France (2011)

  • Volume: 139, Issue: 4, page 519-534
  • ISSN: 0037-9484

Abstract

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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).

How to cite

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D. Sokal, Alan. "When is a Riesz distribution a complex measure?." Bulletin de la Société Mathématique de France 139.4 (2011): 519-534. <http://eudml.org/doc/272580>.

@article{D2011,
abstract = {Let $\mathcal \{R\}_\alpha $ be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by $\alpha \in \mathbb \{C\}$. I give an elementary proof of the necessary and sufficient condition for $\mathcal \{R\}_\alpha $ to be a locally finite complex measure (= complex Radon measure).},
author = {D. Sokal, Alan},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Riesz distribution; Jordan algebra; symmetric cone; Gindikin’s theorem; Wallach set; tempered distribution; positive measure; Radon measure; relatively invariant measure; Laplace transform},
language = {eng},
number = {4},
pages = {519-534},
publisher = {Société mathématique de France},
title = {When is a Riesz distribution a complex measure?},
url = {http://eudml.org/doc/272580},
volume = {139},
year = {2011},
}

TY - JOUR
AU - D. Sokal, Alan
TI - When is a Riesz distribution a complex measure?
JO - Bulletin de la Société Mathématique de France
PY - 2011
PB - Société mathématique de France
VL - 139
IS - 4
SP - 519
EP - 534
AB - Let $\mathcal {R}_\alpha $ be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by $\alpha \in \mathbb {C}$. I give an elementary proof of the necessary and sufficient condition for $\mathcal {R}_\alpha $ to be a locally finite complex measure (= complex Radon measure).
LA - eng
KW - Riesz distribution; Jordan algebra; symmetric cone; Gindikin’s theorem; Wallach set; tempered distribution; positive measure; Radon measure; relatively invariant measure; Laplace transform
UR - http://eudml.org/doc/272580
ER -

References

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