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Ensembles de zéros à la frontière de fonctions analytiques dans des domaines strictement pseudo-convexes

Anne-Marie Chollet (1976)

Annales de l'institut Fourier

Soit D , un domaine borné, strictement pseudo-convexe de C n , on note A ( D ) , la classe des fonctions analytiques dans D , continues ainsi que toutes leurs dérivées dans D . Le principal résultat de ce travail est une condition suffisante pour qu’un sous-ensemble fermé de la frontière de D soit l’ensemble des zéros d’une fonction F de A ( D ) et aussi l’ensemble des zéros communs à F et à toutes ses dérivées.

Equivalent characterizations of Bloch functions

Zhangjian Hu (1994)

Colloquium Mathematicae

In this paper we obtain some equivalent characterizations of Bloch functions on general bounded strongly pseudoconvex domains with smooth boundary, which extends the known results in [1, 9, 10].

Essential norm of the difference of composition operators on Bloch space

Ke-Ben Yang, Ze-Hua Zhou (2010)

Czechoslovak Mathematical Journal

Let ϕ and ψ be holomorphic self-maps of the unit disk, and denote by C ϕ , C ψ the induced composition operators. This paper gives some simple estimates of the essential norm for the difference of composition operators C ϕ - C ψ from Bloch spaces to Bloch spaces in the unit disk. Compactness of the difference is also characterized.

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds D ' of pseudoconvex domains D to all of D even in quite simple situations; The spaces A p ( D ' ) : = 𝒪 ( D ' ) L p ( D ' ) are, in general, not at all preserved. Also the image of the Hilbert space A 2 ( D ) under the restriction to D ' can have a very strange structure.

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