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A weighted Plancherel formula II. The case of the ball

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Zhang G.

Studia Mathematica

1992

tom 102

nr 2

103-120

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.

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1 Studia Mathematica

1 Zhang G.

1 1992

Wyniki wyszukiwania

A weighted Plancherel formula II. The case of the ball