Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 813-816

RUBEL'S PROBLEM ON BOUNDED ANALYTIC FUNCTIONS

Arthur A. Danielyan

University of South Florida, Department of Mathematics and Statistics
Tampa, Florida 33620, U.S.A.; adaniely 'at' usf.edu

Abstract. The paper shows that for any G_δ set F of Lebesgue measure zero on the unit circle T there exists a function f ∈ H^∞ such that the radial limits of f exist at each point of T and vanish precisely on F. This solves a problem proposed by Rubel in 1973.

2010 Mathematics Subject Classification: Primary 30H05, 30H10.

Key words: Bounded analytic function, Fatou point, radial limit, Rubel's problem.

Reference to this article: A.A. Danielyan: Rubel's problem on bounded analytic functions. Ann. Acad. Sci. Fenn. Math. 41 (2016), 813-816.

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doi:10.5186/aasfm.2016.4151