Open AccessThe infinite range of infinite Blaschke product
Author(s) -
XinHan Dong,
WenHui Ai,
Hai-Hua Wu
Publication year - 2019
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14672
Subject(s) - algorithm , annotation , computer science , artificial intelligence , type (biology) , geology , paleontology
For an infinite Blaschke product B B , does there necessarily exist δ > 0 \delta >0 such that each w w satisfying | w | > δ |w|>\delta is assumed infinitely often by B B ? Stephenson raised this question in 1979 and then constructed a counterexample in 1988 to prove that the answer to his problem is negative. In this paper, we find two sufficient conditions under which the answer to the problem is positive.