Result concerning the holomorphic extensions In several complex variables
In
several complex variables, the OhsawaâTakegoshi L2 extension theorem is a fundamental result concerning the
holomorphic extension of an
-holomorphic function defined on a bounded
Stein manifold (such as a
pseudoconvexcompact 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
LaplaceâBeltrami operators, but simpler proofs have since been discovered.[2] Many generalizations and similar results exist, and are known as theorems of OhsawaâTakegoshi type.
Ohsawa, Takeo (2017). "On the extension of holomorphic functions VIII â a remark on a theorem of Guan and Zhou". International Journal of Mathematics. 28 (9).
doi:
10.1142/S0129167X17400055.
Ohsawa, Takeo (10 December 2018). Approaches in Several Complex Variables: Towards the OkaâCartan Theory with Precise Bounds. Springer Monographs in Mathematics.
doi:
10.1007/978-4-431-55747-0.
ISBN9784431568513.
Result concerning the holomorphic extensions In several complex variables
In
several complex variables, the OhsawaâTakegoshi L2 extension theorem is a fundamental result concerning the
holomorphic extension of an
-holomorphic function defined on a bounded
Stein manifold (such as a
pseudoconvexcompact 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
LaplaceâBeltrami operators, but simpler proofs have since been discovered.[2] Many generalizations and similar results exist, and are known as theorems of OhsawaâTakegoshi type.
Ohsawa, Takeo (2017). "On the extension of holomorphic functions VIII â a remark on a theorem of Guan and Zhou". International Journal of Mathematics. 28 (9).
doi:
10.1142/S0129167X17400055.
Ohsawa, Takeo (10 December 2018). Approaches in Several Complex Variables: Towards the OkaâCartan Theory with Precise Bounds. Springer Monographs in Mathematics.
doi:
10.1007/978-4-431-55747-0.
ISBN9784431568513.