Please use this identifier to cite or link to this item:
http://hdl.handle.net/10662/10324
Title: | Transfer operators on complex hyperbolic spaces |
Authors: | Boussejra, Abdelhamid Taoufiq, Tahani |
Keywords: | Transfer operator;Hardy spaces;Operador de transferencia;Espacios Hardy |
Issue Date: | 2013 |
Publisher: | Universidad de Extremadura |
Abstract: | Let Bⁿ be the unit ball in the n-dimensional complex space and let Δ be the Bergman Laplacian on it. For λ ∈ ℂ such that |ℜ(i λ)| < n we give explicitly the transfer operator from the space of holomorphic functions Bⁿ onto an eigenspace E_λ^+ (Bⁿ ) of Δ. This answers a question raised by Eymard in [2]. As application, for λ = − iη with 0 < η < n, we get that the classical Hardy space H²(Bⁿ ) is isometrically isomorphic to the space H_λ^₂ (Bⁿ ) = { F ∈ E_ₙ^⁺(Bⁿ ) : sup 0<r<1 ( 1 − r²) [∫_(∂Bⁿ )⎸F(rƟ)|²dƟ ]½< ∞ }: Consequently H_λ^₂ (Bⁿ ) is a Banach space. |
URI: | http://hdl.handle.net/10662/10324 |
Appears in Collections: | Extracta Mathematicae Vol. 28, nº 1 (2013) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
2605-5686_28_1_113.pdf | 127,08 kB | Adobe PDF | View/Open |
This item is licensed under a Creative Commons License