Vol. 54, No. 2, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 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 and interpolation for some spaces of analytic functions in the unit disc

Arne Stray

Vol. 54 (1974), No. 2, 237–251
Abstract

Let U he a bounded open subset of the complex plane C such that U and CU are connected. (If B C,B denotes its closure in C.) H(U) is the space of all bounded analytic functions defined on U. Let S U be She zero set of a nonzero function in H(U). Necessary and sufficient conditions on S are given for the existence of an open sel 0 tU(SS) such that H(0) and H(U) have the same restrictions to S. If U is the unit disc D = {z : |z| < 1} and S is as above, the following result holds for all the Hardy spaces Hp(D), 0 < p ≤∞: Given g Hp(D), there is a function fanalytic in C(SS) such thatf|D Hp(D) andf = g on S.

Mathematical Subject Classification 2000
Primary: 30A78
Secondary: 46J15
Milestones
Received: 21 November 1972
Published: 1 October 1974
Authors
Arne Stray
Mathematics Institute
University of Bergen
5007 Bergen
Norway