Ohsawa–Takegoshi L2 extension theorem: Difference between revisions
Content deleted Content added
Bibcode Bot (talk | contribs) m Adding 0 arxiv eprint(s), 1 bibcode(s) and 0 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot |
Citation bot (talk | contribs) m Removed parameters. | You can use this bot yourself. Report bugs here. | User-activated. |
||
| Line 1: | Line 1: | ||
{{Orphan|date=November 2015}} |
{{Orphan|date=November 2015}} |
||
In [[several complex variables]], the '''Ohsawa–Takegoshi theorem''' is a fundamental result concerning the [[Holomorphic function#Several variables|holomorphic]] extension of a [[Square-integrable function|<math>L^{2}</math>]]-holomorphic function defined on a bounded [[Stein manifold]] (such as a [[pseudoconvex]] [[compact (mathematics)|compact]] set in <math>\mathbb{C}^{n}</math> of dimension less than <math>n</math>) to a domain of higher dimension, with a bound on the growth. It was discovered by [[Takeo Ohsawa]] and Kensho Takegoshi in 1987,<ref name="OT1987">{{cite journal |
In [[several complex variables]], the '''Ohsawa–Takegoshi theorem''' is a fundamental result concerning the [[Holomorphic function#Several variables|holomorphic]] extension of a [[Square-integrable function|<math>L^{2}</math>]]-holomorphic function defined on a bounded [[Stein manifold]] (such as a [[pseudoconvex]] [[compact (mathematics)|compact]] set in <math>\mathbb{C}^{n}</math> of dimension less than <math>n</math>) to a domain of higher dimension, with a bound on the growth. It was discovered by [[Takeo Ohsawa]] and Kensho Takegoshi in 1987,<ref name="OT1987">{{cite journal | title=On the extension of L2 holomorphic functions |author1=Ohsawa, T. |author2=Takegoshi, K. | journal=[[Mathematische Zeitschrift]] | year=1987 | volume=195 | issue=2 | pages=197–204 | doi=10.1007/BF01166457}}</ref> using what have been described as ''ad hoc'' methods involving twisted [[Laplace–Beltrami operator]]s, but simpler proofs have since been discovered.<ref name="Siu2011">{{cite journal | title=Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles | author=Siu, Y. T. | journal=Science China Mathematics |date=August 2011 | volume=54 | issue=8 | pages=1767–1802 | doi=10.1007/s11425-011-4293-7| arxiv=1104.2563 | bibcode=2011ScChA..54.1767S }}</ref> Many generalizations and similar results exist, and are known as theorems of Ohsawa-Takegoshi type. |
||
==References== |
==References== |
||
Revision as of 11:33, 8 January 2019
In several complex variables, the Ohsawa–Takegoshi theorem is a fundamental result concerning the holomorphic extension of a -holomorphic function defined on a bounded Stein manifold (such as a pseudoconvex compact set in of dimension less than ) to a domain of higher dimension, with a bound on the growth. It was discovered by Takeo Ohsawa and Kensho Takegoshi in 1987,[1] using what have been described as ad hoc methods involving twisted Laplace–Beltrami operators, but simpler proofs have since been discovered.[2] Many generalizations and similar results exist, and are known as theorems of Ohsawa-Takegoshi type.
References
- ^ Ohsawa, T.; Takegoshi, K. (1987). "On the extension of L2 holomorphic functions". Mathematische Zeitschrift. 195 (2): 197–204. doi:10.1007/BF01166457.
- ^ Siu, Y. T. (August 2011). "Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles". Science China Mathematics. 54 (8): 1767–1802. arXiv:1104.2563. Bibcode:2011ScChA..54.1767S. doi:10.1007/s11425-011-4293-7.