# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## A weighted Plancherel formula II. The case of the ball

### Tom 102 / 1992

Studia Mathematica 102 (1992), 103-120 DOI: 10.4064/sm-102-2-103-120

#### Streszczenie

The group SU(1,d) acts naturally on the Hilbert space $L²(B dμ_α) (α > -1)$, where B is the unit ball of $ℂ^d$ and $dμ_α$ the weighted measure $(1-|z|²)^α dm(z)$. 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.

• Genkai Zhang

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek