- Tytuł:
- A weighted Plancherel formula II. The case of the ball
- Autorzy:
- Zhang, Genkai
- Powiązania:
- https://bibliotekanauki.pl/articles/1293186.pdf
- Data publikacji:
- 1992
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Plancherel formula
Harish-Chandra c-function
reproducing kernel
orthogonal polynomial
invariant Cauchy-Riemann operator - Opis:
- 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.
- Źródło:
-
Studia Mathematica; 1992, 102, 2; 103-120
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł