miun.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On the Hartogs extension theorem for unbounded domains in Cn
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. (Mathematics)
Arizona State University, Tempe, AZ, U.S.A.
Cardinal Stefan Wyszy´nski University, Warsaw, Poland.
2018 (English)Report (Other academic)
Abstract [en]

Let Ω ⊂ Cn, n ≥ 2, be a domain with smooth connected boundary. IfΩ is relatively compact, the Hartogs-Bochner theorem ensures that everyCR distribution on ∂Ω has a holomorphic extension to Ω. For unboundeddomains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extensionproperty holds if and only if the envelope of holomorphy of Cn\Ω is Cn.It seems that it is a first result in the literature which gives a geometriccharacterization of unbounded domains in Cnfor which the Hartogs phenomenon holds. Comparing this to earlier work by the first two authorsand Z. S lodkowski, one observes that the extension problem sensitively depends on a finer geometry of the contact of a complex hypersurface andthe boundary of the domain.

Place, publisher, year, edition, pages
2018. , p. 21
Series
Mid Sweden Mathematical Reports ; 3
Keywords [en]
complex analysis, envelopes of holomorphy, CR functions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:miun:diva-35286ISBN: 978-91-88527-87-5 (print)OAI: oai:DiVA.org:miun-35286DiVA, id: diva2:1272209
Available from: 2018-12-18 Created: 2018-12-18 Last updated: 2018-12-19Bibliographically approved

Open Access in DiVA

BoggessDwilewiczPorten2018(418 kB)100 downloads
File information
File name FULLTEXT01.pdfFile size 418 kBChecksum SHA-512
61c01e7aa0d2507c325c4ebb5b32395198bb19034cbf5586fcd486b981b03fc64ef27a92754001b076bfffd6374bd38d9cf089c67c400e9282bd6808b6e57345
Type fulltextMimetype application/pdf

Authority records BETA

Porten, Egmont

Search in DiVA

By author/editor
Porten, Egmont
By organisation
Department of Mathematics and Science Education
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 100 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 105 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf