Vol. 80, No. 1, 1979

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Approximation by rational modules on nowhere dense sets

James Li-Ming Wang

Vol. 80 (1979), No. 1, 293–295
Abstract

Let X be a compact subset of the complex plane. Let the module (X)𝒫m be the space of all functions of the form

r0(z) + r1(z)z + ⋅⋅⋅+ rmzm

where each ri is a rational function with poles off X. We prove that (X)𝒫1 is dese in Lp(X) for all 1 p < and (X)𝒫2 is dense in 𝒞(X) if X has no interior point. As corollaries, we also prove that (X)𝒫2 is dense in lip (α,X) for all 0 < α < 1 and (X)𝒫3 is dense in D1(X) for the same X.

Mathematical Subject Classification 2000
Primary: 30E10
Milestones
Received: 17 May 1978
Revised: 10 August 1978
Published: 1 January 1979
Authors
James Li-Ming Wang