Analytic capacity and projections
نویسندگان
چکیده
منابع مشابه
Areas of Projections of Analytic Sets
If V is a pure 1-dimensional analytic subvariety of C", then the area of V is the sum of the areas, counting multiplicity, of the projections of V onto the n coordinate lines [5, 6]. If V is a pure 1-dimensional variety in the unit ball in C" which passes through the origin, then [5] the area of V is at least ~. Together these theorems imply that a 1variety through 0 in the unit ball has the pr...
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A compact set E ⊂ C is said to be removable for bounded analytic functions if for any open set containing E, every bounded function analytic on \ E has an analytic extension to . Analytic capacity is a notion that, in a sense, measures the size of a set as a non removable singularity. In particular, a compact set is removable if and only if its analytic capacity vanishes. The so-called Painlevé...
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For K ⊂ C compact, we say that K has vanishing analytic capacity (or γ(K) = 0) when all bounded analytic functions on C\K are constant. We would like to characterize γ(K) = 0 geometrically. Easily, γ(K) > 0 when K has Hausdorff dimension larger than 1, and γ(K) = 0 when dim(K) < 1. Thus only the case when dim(K) = 1 is interesting. So far there is no characterization of γ(K) = 0 in general, but...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2020
ISSN: 1435-9855
DOI: 10.4171/jems/1004