Displaying similar documents to “Iterates and the boundary behavior of the Berezin transform”

A result on extension of C.R. functions

Makhlouf Derridj, John Erik Fornaess (1983)

Annales de l'institut Fourier

Similarity:

Let Ω an open set in C 4 near z 0 Ω , λ a suitable holomorphic function near z 0 . If we know that we can solve the following problem (see [M. Derridj, Annali. Sci. Norm. Pisa, Série IV, vol. IX (1981)]) : u = λ f , ( f is a ( 0 , 1 ) form, closed in U ( z 0 ) in U ( z 0 ) with supp ( u ) Ω U ( z 0 ) , then we deduce an extension result for C . R . functions on Ω U ( z 0 ) , as holomorphic fonctions in Ω V ( z 0 ) .

A triple ratio on the Silov boundary of a bounded symmetric domain

Jean-Louis Clerc (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Let D be a Hermitian symmetric space of tube type, S its Silov boundary and G the neutral component of the group of bi-holomorphic diffeomorphisms of D . Our main interest is in studying the action of G on S 3 = S × S × S . Sections 1 and 2 are part of a joint work with B. Ørsted (see [4]). In Section 1, as a pedagogical introduction, we study the case where D is the unit disc and S is the circle. This is a fairly elementary and explicit case, where one can easily get a flavour of the more general results....

The exceptional sets for functions of the Bergman space in the unit ball

Piotr Jakóbczak (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Let D be a domain in C 2 . Given w C , set D w = z C z , w D . If f is a holomorphic and square-integrable function in D , then the set E D , f of all w such that f ( , w ) is not square-integrable in D w has measure zero. We call this set the exceptional set for f . In this Note we prove that whenever 0 < r < 1 there exists a holomorphic square-integrable function f in the unit ball B in C 2 such that E B , f is the circle C 0 , r = z C z = r .

Biholomorphic maps determined on the boundary

Nozomu Mochizuki (1977)

Annales de l'institut Fourier

Similarity:

Let D be a bounded domain in C n such that the boundary b D is topologically S 2 n - 1 in R 2 n with a regular point; let f : D ˜ C n be a holomorphic map where D ˜ is a neighborhood of D . If f is one-to-one when restricted to b D , then f : D f ( D ) is biholomorphic.