Displaying similar documents to “Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map.”

Boundary cross theorem in dimension 1

Peter Pflug, Viêt-Anh Nguyên (2007)

Annales Polonici Mathematici

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Let X, Y be two complex manifolds of dimension 1 which are countable at infinity, let D ⊂ X, G ⊂ Y be two open sets, let A (resp. B) be a subset of ∂D (resp. ∂G), and let W be the 2-fold cross ((D∪A)×B) ∪ (A×(B∪G)). Suppose in addition that D (resp. G) is Jordan-curve-like on A (resp. B) and that A and B are of positive length. We determine the "envelope of holomorphy" Ŵ of W in the sense that any function locally bounded on W, measurable on A × B, and separately holomorphic on (A ×...

Bounded holomorphic functions with multiple sheeted pluripolar hulls

Armen Edigarian, Józef Siciak, Włodzimierz Zwonek (2006)

Studia Mathematica

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We describe compact subsets K of ∂𝔻 and ℝ admitting holomorphic functions f with the domains of existence equal to ℂ∖K and such that the pluripolar hulls of their graphs are infinitely sheeted. The paper is motivated by a recent paper of Poletsky and Wiegerinck.

Vector-valued holomorphic and harmonic functions

Wolfgang Arendt (2016)

Concrete Operators

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Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic...

Extension of vector-valued holomorphic and harmonic functions

José Bonet, Leonhard Frerick, Enrique Jordá (2007)

Studia Mathematica

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We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak*-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.

Rigidity of harmonic measure

I. Popovici, Alexander Volberg (1996)

Fundamenta Mathematicae

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Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical...