Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley
Chadli, Mohammed
Annales de l'Institut Fourier, Tome 48 (1998), p. 97-132 / Harvested from Numdam
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Dans cet article, en utilisant les algèbres de Jordan euclidiennes, nous étudions l’espace de Hardy H 2 (Ξ) d’un espace symétrique de type Cayley ℳ=G/H. Nous montrons que le noyau de Cauchy-Szegö de H 2 (Ξ) s’exprime comme somme d’une série faisant intervenir la fonction c de Harish-Chandra de l’espace symétrique riemannien D=G/K, la fonction c de l’espace symétrique c-dual 𝒩 de ℳ et les fonctions sphériques de l’espace symétrique ordonné 𝒩. Nous établissons, dans le cas où la dimension de l’algèbre de Jordan associée à ℳ est un multiple de son rang, un isomorphisme entre l’espace de Hardy H 2 (Ξ) (non-commutatif) et l’espace de Hardy classique H 2 (D×D) (commutatif) du bi-disque. Nous obtenons ainsi une deuxième formule pour le noyau de Cauchy-Szegö.

In this paper, by using the Euclidean Jordan algebras, we study the Hardy space H 2 (Ξ) of a symmetric space of Cayley type ℳ=G/H. We show that the Cauchy-Szegö kernel of H 2 (Ξ) expresses as a series using the Harish-Chandra c-function of the Riemannian symmetric space D=G/K, the c-function of the c-dual symmetric space 𝒩 of ℳ and spherical functions of the ordered symmetric space 𝒩. We give, in the case of the dimension of the Jordan algebra associated to ℳ being a multiple of its rank, the relation between the (non-commutative) Hardy space H 2 (Ξ) and the classical (commutative) Hardy space H 2 (D×D) of the bidisc. And we obtain another formula for the Cauchy-Szegö kernel.

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     author = {Chadli, Mohammed},
     title = {Noyau de Cauchy-Szeg\"o d'un espace sym\'etrique de type Cayley},
     journal = {Annales de l'Institut Fourier},
     volume = {48},
     year = {1998},
     pages = {97-132},
     doi = {10.5802/aif.1612},
     mrnumber = {99b:22022},
     zbl = {0920.43008},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIF_1998__48_1_97_0}
}

Chadli, Mohammed. Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley. Annales de l'Institut Fourier, Tome 48 (1998) pp. 97-132. doi : 10.5802/aif.1612. http://gdmltest.u-ga.fr/item/AIF_1998__48_1_97_0/

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