Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The traces of holomorphic functions on real submanifolds


Author: Gary Alvin Harris
Journal: Trans. Amer. Math. Soc. 242 (1978), 205-223
MSC: Primary 32C05
MathSciNet review: 0477120
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose M is a real-analytic submanifold of complex Euclidean n = space and consider the following question: Given a real-analytic function f defined on M, is f the restriction to M of an ambient holomorphic function? If M is a C.R. submanifold the question has been answered completely. Namely, f is the trace of a holomorphic function if and only if f is a C.R. function. The more general situation in which M need not be a C.R. submanifold is discussed in this paper.

A complete answer is obtained in case the dimension of M is larger than or equal to n and M is generic in some neighborhood of each point off its C.R. singularities. The solution is of infinite order and follows from a consideration of the following problem: Given a holomorphic function f and a holomorphic mapping $ \Phi$, when does there exist a holomorphic mapping F such that $ f = F \circ \Phi $?


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32C05

Retrieve articles in all journals with MSC: 32C05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0477120-1
PII: S 0002-9947(1978)0477120-1
Keywords: Holomorphic trace, real-analytic submanifold of $ {{\textbf{C}}^n}$
Article copyright: © Copyright 1978 American Mathematical Society