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Title: Transfer operators on complex hyperbolic spaces
Authors: Boussejra, Abdelhamid
Taoufiq, Tahani
metadata.dc.contributor.advisor: Université Ibn Tofail. Maroc
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.
Appears in Collections:Extracta Mathematicae Vol. 28, nº 1 (2013)

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