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Semi-groupe de Lie associé à un cône symétrique

Khalid Koufany — 1995

Annales de l'institut Fourier

Soit V une algèbre de Jordan simple euclidienne de dimension finie et Ω le cône symétrique associé. Nous étudions dans cet article le semi-groupe Γ , naturellement associé à V , formé des automorphismes holomorphes du domaine tube T Ω : = V + i Ω qui appliquent le cône Ω dans lui-même.

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Khalid KoufanyBent Ørsted — 1996

Annales de l'institut Fourier

For the scalar holomorphic discrete series representations of SU ( 2 , 2 ) and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside SU ( 2 , 2 ) . We construct a Cayley transform between the Ol’shanskiĭ semigroup having U ( 1 , 1 ) as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for SU ( 2 , 2 ) . This allows calculating the composition series in terms of harmonic analysis on U ( 1 , 1 ) . In particular we show that the Ol’shanskiĭ Hardy space for U ( 1 , 1 ) is different...

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