Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T16:16:28.891Z Has data issue: false hasContentIssue false
  • English
  • Français

algebras generated by holomorphic and harmonic functions on the disc

Published online by Cambridge University Press:  23 September 2005

alexander j. izzo
alexander j. izzo
Affiliation:
department of mathematics and statistics, bowling green state university, bowling green, oh 43403, usaaizzo@math.bgsu.edu current address: department of mathematics, brown university, box 1917, providence, ri 02912, usa
Get access

Abstract

let $e$ be a subset of the boundary of the open unit disc $d$, and let $a$ be the algebra of bounded holomorphic functions on $d$ that extend continuously to $d \cup e$. it is shown that if $f$ is a bounded harmonic function on $d$ that extends continuously to $d \cup e$ and is not holomorphic, then the uniformly closed algebra $a[f]$ generated by $a$ and $f$ contains $c({\overline{d}})$. this result contains as special cases a result on the disc algebra due to čirka and a result on $h^{\infty}(d)$ due to axler and shields. a stronger form of the result, in which $f$ is allowed to have discontinuities on a small subset of $e$, is also established.

Keywords

46j1046j1530h05
Type
papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 5 , October 2005 , pp. 761 - 770
Copyright
the london mathematical society 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

this paper was presented to the american mathematical society in preliminary form, on october 13, 2002, under the title interpolating between a theorem of čirka and a theorem of axler and shields.