On Semiclassical Ohsawa-Takegoshi Extension Theorem

For a fixed complex submanifold in a complex manifold, we consider the operator which associates to a given holomorphic section of a positive line bundle over the submanifold the holomorphic extension of it to the ambient manifold with the minimal \(L^2\) -norm. When the tensor power of the line bundle tends to infinity, we obtain an explicit asymptotic formula for this extension operator and derive several consequences of this study.