The traces of holomorphic functions on real submanifolds
Author:
Gary Alvin Harris
Journal:
Trans. Amer. Math. Soc. 242 (1978), 205223
MSC:
Primary 32C05
MathSciNet review:
0477120
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Suppose M is a realanalytic submanifold of complex Euclidean n = space and consider the following question: Given a realanalytic 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 , when does there exist a holomorphic mapping F such that ?
 [EH]
Paul
M. Eakin and Gary
A. Harris, When 𝐹(𝑓) convergent implies 𝑓
is convergent, Math. Ann. 229 (1977), no. 3,
201–210. MR 0444651
(56 #3001)
 [GR]
H.
Grauert and R.
Remmert, Analytische Stellenalgebren, SpringerVerlag,
BerlinNew York, 1971 (German). Unter Mitarbeit von O. Riemenschneider; Die
Grundlehren der mathematischen Wissenschaften, Band 176. MR 0316742
(47 #5290)
 [T]
Giuseppe
Tomassini, Tracce delle funzioni olomorfe sulle sottovarietà
analitiche reali d’una varietà complessa, Ann. Scuola
Norm. Sup. Pisa (3) 20 (1966), 31–43 (Italian). MR 0206992
(34 #6808)
 [EH]
 Paul Eakin and Gary Harris, When convergent implies f is convergent, Math. Ann. 229 (1977), 211221. MR 0444651 (56:3001)
 [GR]
 Hans Grauert and Reinhold Remmert, Analytische Stellenalgebren, SpringerVerlag, New York, 1970. MR 0316742 (47:5290)
 [T]
 Giuseppe Tomassini, Trace delle funzioni olomorfe sulle sottovarieta analitiche reali d'una varieta complessa, Ann. Scuola Norm. Sup. Pisa 20 (1966), 3143. MR 0206992 (34:6808)
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/S00029947197804771201
PII:
S 00029947(1978)04771201
Keywords:
Holomorphic trace,
realanalytic submanifold of
Article copyright:
© Copyright 1978
American Mathematical Society
