Displaying similar documents to “A weighted Plancherel formula. III. The case of the hyperbolic matrix ball.”

A weighted Plancherel formula II. The case of the ball

Genkai Zhang (1992)

Studia Mathematica

Similarity:

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 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...