Identificador persistente para citar o vincular este elemento:
http://hdl.handle.net/10662/10324
Títulos: | Transfer operators on complex hyperbolic spaces |
Autores/as: | Boussejra, Abdelhamid Taoufiq, Tahani |
Palabras clave: | Transfer operator;Hardy spaces;Operador de transferencia;Espacios Hardy |
Fecha de publicación: | 2013 |
Editor/a: | Universidad de Extremadura |
Resumen: | 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 |
Colección: | Extracta Mathematicae Vol. 28, nº 1 (2013) |
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