Vol. 65, No. 1, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Sobolev approximation by a sum of subalgebras on the circle

John Brady Garnett and Anthony G. O’Farrell

Vol. 65 (1976), No. 1, 55–63
Abstract

Let ψ be an orientation-reversing homeomorphism of the unit circle onto itself. We consider approximation in certain Sobolev norms by functions of the form f(z) + g(ψ), where f and g are polynomials. The methods involve conformal welding and Hardy space theory. We construct a Jordan arc of positive continuous analytic capacity such that the harmonic measures for the two complementary domains are mutually absolutely continuous.

Mathematical Subject Classification
Primary: 30A82, 30A82
Milestones
Received: 14 April 1975
Revised: 18 February 1976
Published: 1 July 1976
Authors
John Brady Garnett
Department of Mathematics
University of California
Los Angeles CA 90024
United States
Anthony G. O’Farrell