Extracta Mathematicae Vol. 28, nº 1 (2013)
http://hdl.handle.net/10662/10265
2020-06-03T10:13:11ZTransfer operators on complex hyperbolic spaces
http://hdl.handle.net/10662/10324
Transfer operators on complex hyperbolic spaces
Boussejra, Abdelhamid; Taoufiq, Tahani
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.
2013-01-01T00:00:00ZContinuity of the norm of composition operators
http://hdl.handle.net/10662/10321
Continuity of the norm of composition operators
Wolf, Elke
Let ϕ be an analytic self-map of the open unit disk ⅅin the complex plane. Such a map induces a composition operator C_ϕ on weighted Banach spaces of holomorphic functions. We study when the norm of composition operators acting on weighted Banach spaces of analytic functions is continuous at a symbol.
2013-01-01T00:00:00ZWeyl type theorems for restrictions of bounded linear operators
http://hdl.handle.net/10662/10320
Weyl type theorems for restrictions of bounded linear operators
Carpintero, C.; García, O.; Muñoz, D.; Rosas, E.; Sanabria, J.
In this paper we give sufficient conditions for which Weyl’s theorems for a bounded linear operator T, acting on a Banach space X, can be reduced to the study of Weyl’s theorems for some restriction of T.
2013-01-01T00:00:00ZA characterization of the essential pseudospectra and application to a transport equation
http://hdl.handle.net/10662/10319
A characterization of the essential pseudospectra and application to a transport equation
Ammar, Aymen; Jeribi, Aref
In this paper, we introduce and study the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of this essential pseudospectra. The obtained results are used to describe the essential pseudospectra of transport operators.
2013-01-01T00:00:00Z