In several complex variables, the Ohsawa–Takegoshi L2 extension theorem is a fundamental result concerning the holomorphic extension of an
-holomorphic function defined on a bounded Stein manifold (such as a pseudoconvex compact set in
) 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.