When is a Riesz distribution a complex measure?
Bulletin de la Société Mathématique de France, Volume 139 (2011) no. 4, p. 519-534

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

Soit α la distribution de Riesz sur une algèbre de Jordan euclidienne simple, paramétrisée par α. Je donne une démonstration élémentaire de la condition nécessaire et suffisante pour que α soit une mesure complexe localement finie (= mesure de Radon complexe).

DOI : https://doi.org/10.24033/bsmf.2617
Classification:  43A85,  17A15,  17C99,  28C10,  44A10,  46F10,  47G10,  60E05,  62H05
Keywords: Riesz distribution, Jordan algebra, symmetric cone, Gindikin's theorem, Wallach set, tempered distribution, positive measure, Radon measure, relatively invariant measure, Laplace transform
@article{BSMF_2011__139_4_519_0,
     author = {D.~Sokal, Alan},
     title = {When is a Riesz distribution a complex measure?},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {139},
     number = {4},
     year = {2011},
     pages = {519-534},
     doi = {10.24033/bsmf.2617},
     zbl = {1263.43003},
     mrnumber = {2869303},
     language = {en},
     url = {http://www.numdam.org/item/BSMF_2011__139_4_519_0}
}
When is a Riesz distribution a complex measure?. Bulletin de la Société Mathématique de France, Volume 139 (2011) no. 4, pp. 519-534. doi : 10.24033/bsmf.2617. http://www.numdam.org/item/BSMF_2011__139_4_519_0/

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