L2-Concrete Spectral Analysis of the Invariant LaplacianΔαβin the Unit Complex BallBn
✍ Scribed by Adbelhamid Boussejra; Ahmed Intissar
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 380 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
For every fixed real number * related to the continuous spectrum of the invariant Laplacians
2 z j zÄ j +: : n j=1 z j z j +; : n j=1 zÄ j zÄ j &:; = in B n , we characterize the eigenfunctions of 2 :; that are Poisson integrals of L 2 -functions on the boundary of B n . These eigenfunctions occurred in the weighted Plancherel formula of the unit complex ball. (See Zhang, Studia Math. 102 (2) (1992), for the weighted Plancherel formula in the ball.) The obtained characterization generalizes our announced result in Boussejra and Intissar, C. R. Acad. Sci. 315 1992), 1353 1357, for the Bergman Laplacian 2 00 of the unit complex ball to the Laplacians 2 :; , for arbitrary :, ; in R.