Search results for "Holomorphic function"

Boundedness of composition operators in holomorphic Hölder type spaces

2021

Mean ergodic composition operators on Banach spaces of holomorphic functions

2016

[EN] Given a symbol cc, i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator C-phi(f) = f circle phi defined on the Banach spaces of holomorphic functions A(D) and H-infinity(D). We obtain different conditions on the symbol phi which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behavior of the iterates of the symbol. Finally, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.

Spaces of holomorphic functions in regular domains

2009

AbstractLet Ω be a regular domain in the complex plane C, Ω≠C. Let Gb(Ω) be the linear space over C of the holomorphic functions f in Ω such that f(n) is bounded in Ω and is continuously extendible to the closure Ω¯ of Ω, n=0,1,2,… . We endow Gb(Ω), in a natural manner, with a structure of Fréchet space and we obtain dense subspaces F of Gb(Ω), with good topological linear properties, also satisfying that each function f of F, distinct from zero, does not extend holomorphically outside Ω.

Holomorphic Maps and Pencils of Circles

2008

(2008). Holomorphic Maps and Pencils of Circles. The American Mathematical Monthly: Vol. 115, No. 8, pp. 690-700.

The Composition Operation on Spaces of Holomorphic Mappings

2020

AbstractWe discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.

Holomorphic Hölder‐type spaces and composition operators

2020

On transversely holomorphic flows I

1996

ALGEBRAS OF SYMMETRIC HOLOMORPHIC FUNCTIONS ON ${\cal L}_p$

2003

Sur les polaires de certaines 1-formes

1998

Resume Nous enoncons, sous certaines conditions, une propriete de coincidence des branches polaires generiques d'une 1-forme holomorphe avec ses separatrices et ses polaires exceptionnelles.

Comparison theorems for the volume of a complex submanifold of a Kaehler manifold

1990

LetM be a Kaehler manifold of real dimension 2n with holomorphic sectional curvatureK H≥4λ and antiholomorphic Ricci curvatureρ A≥(2n−2)λ, andP is a complex hypersurface. We give a bound for the quotient (volume ofP)/(volume ofM) and prove that this bound is attained if and only ifP=C P n−1(λ) andM=C P n(λ). Moreover, we give some results on the volume of of tubes aboutP inM.