Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/3944
Title: Functions Holomorphic along Holomorphic Vector Fields
Contributor(s): Kim, Kang-Tae (author); Poletsky, Evgeny (author); Schmalz, Gerd  (author)orcid 
Publication Date: 2009
DOI: 10.1007/s12220-009-9078-7
Handle Link: https://hdl.handle.net/1959.11/3944
Abstract: The main result of the paper is the following generalization of Forelli's theorem (Math. Scand. 41:358–364, 1977): Suppose 'F' is a holomorphic vector field with singular point at 'p', such that 'F' is linearizable at 'p' and the matrix is diagonalizable with eigenvalues whose ratios are positive reals. Then any function φ that has an asymptotic Taylor expansion at 'p' and is holomorphic along the complex integral curves of 'F' is holomorphic in a neighborhood of 'p'. We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary.
Publication Type: Journal Article
Source of Publication: Journal of Geometric Analysis, 19(3), p. 655-666
Publisher: Springer New York LLC
Place of Publication: United States of America
ISSN: 1050-6926
Field of Research (FOR): 010111 Real and Complex Functions (incl Several Variables)
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Statistics to Oct 2018: Visitors: 134
Views: 136
Downloads: 0
Appears in Collections:Journal Article

Files in This Item:
2 files
File Description SizeFormat 
Show full item record

SCOPUSTM   
Citations

4
checked on Nov 30, 2018

Page view(s)

62
checked on Mar 1, 2019
Google Media

Google ScholarTM

Check

Altmetric


Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.