A weighted Plancherel formula II. The case of the ball

Zhang, Genkai

Zhang, Genkai

Studia Mathematica, Tome 103 (1992), p. 103-120 / Harvested from The Polish Digital Mathematics Library

Résumé

The group SU(1,d) acts naturally on the Hilbert space $L ² (B d μ_{α}) (α > - 1)$ , where B is the unit ball of $ℂ^{d}$ and $d μ_{α}$ the weighted measure ${(1 - | z | ²)}^{α} d m (z)$ . It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic tensor fields.

Publié le : 1992-01-01

Zbl 0811.43003

EUDML-ID : urn:eudml:doc:215917

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     author = {Genkai Zhang},
     title = {A weighted Plancherel formula II. The case of the ball},
     journal = {Studia Mathematica},
     volume = {103},
     year = {1992},
     pages = {103-120},
     zbl = {0811.43003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv102i2p103bwm}
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Zhang, Genkai. A weighted Plancherel formula II. The case of the ball. Studia Mathematica, Tome 103 (1992) pp. 103-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i2p103bwm/

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