### 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 |

State | Published - 2011 |

### Fingerprint

### 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

- Mathematics(all)

### Cite this

*Bulletin de la Societe Mathematique de France*,

*139*(4), 519-534.

**When is a riesz distribution a complex measure?** / Sokal, Alan D.

Research output: Contribution to journal › Article

*Bulletin de la Societe Mathematique de France*, vol. 139, no. 4, pp. 519-534.

}

TY - JOUR

T1 - When is a riesz distribution a complex measure?

AU - Sokal, Alan D.

PY - 2011

Y1 - 2011

N2 - 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).

AB - 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).

KW - Gindikin's theorem

KW - Jordan algebra

KW - Laplace transform

KW - Positive measure

KW - Radon measure

KW - Relatively invariant measure

KW - Riesz distribution

KW - Symmetric cone

KW - Tempered distribution

KW - Wallach set

UR - http://www.scopus.com/inward/record.url?scp=84862093731&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862093731&partnerID=8YFLogxK

M3 - Article

VL - 139

SP - 519

EP - 534

JO - Bulletin de la Societe Mathematique de France

JF - Bulletin de la Societe Mathematique de France

SN - 0037-9484

IS - 4

ER -