English

Rubel's problem on bounded analytic functions

Complex Variables 2016-06-13 v1

Abstract

The paper shows that for any GδG_\delta set FF of Lebesgue measure zero on the unit circle TT there exists a function fHf \in H^{\infty} such that the radial limits of ff exist at each point of TT and vanish precisely on FF. This solves a problem proposed by Lee Rubel in 1973.

Cite

@article{arxiv.1606.03116,
  title  = {Rubel's problem on bounded analytic functions},
  author = {Arthur A. Danielyan},
  journal= {arXiv preprint arXiv:1606.03116},
  year   = {2016}
}
R2 v1 2026-06-22T14:22:06.140Z