Algebras generated by two bounded holomorphic functions
Complex Variables
2007-05-23 v2 Classical Analysis and ODEs
Abstract
We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.
Cite
@article{arxiv.math/0101171,
title = {Algebras generated by two bounded holomorphic functions},
author = {Michael I. Stessin and Pascal J. Thomas},
journal= {arXiv preprint arXiv:math/0101171},
year = {2007}
}
Comments
22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematique