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Brownian motion and generalized analytic and inner functions

Alain Bernard, Eddy A. Campbell, A. M. Davie (1979)

Annales de l'institut Fourier

Let f be a mapping from an open set in R p into R q , with p > q . To say that f preserves Brownian motion, up to a random change of clock, means that f is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case p = 2 , q = 2 , such conditions signify that f corresponds to an analytic function of one complex variable. We study, essentially that case p = 3 , q = 2 , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for p = 4 , q = 2 would solve...

Cluster sets of analytic multivalued functions

S. Harbottle (1992)

Studia Mathematica

Classical theorems about the cluster sets of holomorphic functions on the unit disc are extended to the more general setting of analytic multivalued functions, and examples are given to show that these extensions cannot be improved.

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