Vol. 33, No. 1, 1970

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
Tangential Cauchy-Riemann equations and uniform approximation

Michael Benton Freeman

Vol. 33 (1970), No. 1, 101–108
Abstract

A smooth (𝒞) function on a smooth real submanifold M of complex Euclidean space Cn is a CR function if it satisfies the Cauchy-Riemann equations tangential to M. It is shown that each CR function admits an extension to an open neighborhood of M in Cn whose z-derivatives all vanish on M to a prescribed high order, provided that the system of tangential Cauchy-Riemann equations has minimal rank throughout M. This result is applied to show that on a holomorphically convex compact set in M each CR fuction can be uniformly approximated by holomorphic functions.

Mathematical Subject Classification
Primary: 32.70
Milestones
Received: 21 November 1969
Published: 1 April 1970
Authors
Michael Benton Freeman