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Boundary uniqueness theorems for meromorphic functions. (English. Russian original) Zbl 0691.30025

Math. USSR, Sb. 61, No. 2, 321-334 (1988); translation from Mat. Sb., Nov. Ser. 133(175), No. 3, 325-340 (1987).
Summary: A study is made of sets of uniqueness for the class of arbitrary meromorphic functions on the disk and for the limit values over h-angles (domains with zero angle on the boundary and with form determined by a function h(x)). The sets of uniqueness are characterized with the help of the concepts of h-indecomposability of h-regularity, introduced and studied in this article. These concepts turn out to be intermediate between measure and category. The concept of the porosity of a set served as a starting point for the definition of the property of h- indecomposability. The central result in this paper is the following theorem. Let \({\mathcal F}\) be the class of all meromorphic functions f(z) on the unit disk. A set E on the boundary of the disk is a set of uniqueness for the class \({\mathcal F}\) and for the limit values over h-angles if and only if E is h-indecomposable.

MSC:

30D40 Cluster sets, prime ends, boundary behavior
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