Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419356 | Journal of Mathematical Analysis and Applications | 2011 | 7 Pages |
Abstract
We give an elementary and direct proof of the identity:limâsup|w|â1âNÏ(w)1â|w|=limâsup|a|â1â(1â|a|2)â1/(1âa¯Ï)âH22, for any analytic self-map Ï of {z:|z|<1}; where NÏ denotes the Nevanlinna counting function of Ï. We further show that one can find analytic self-maps Ï of {z:|z|<1}, where the composition operator CÏ on the Hardy space H2 is compact, such that âÏnâH2 tends to zero at an arbitrarily slow rate, as nââ; even in the case that Ï is univalent. Among these are new examples, where CÏ is compact on H2, but not in any of the Schatten classes.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
John R. Akeroyd,