On holomorphic extension of hyperfunctions
One of the consequences of the Bochner-Hartogs theorem is that every CR- function \(f\) defined on the boundary \(\partial \Omega\) of a bounded domain \(\Omega\) in \(\mathbb{C}^ n\) \((n > 1)\) is holomorphically extendable onto \(\Omega\) provided \(\partial \Omega\) is connected. In the case \(f\) is a hyperfunction on \(\partial \Omega\), the existence of a holomorphic extension was also proved. There is another generalization of the Bochner-Hartogs theorem, due to the author in collaboration with some others, which says that the function \(f\) needs only to be orthogonal to the Bochner-Martinelli kernels. In the present paper an analogue of this last version of the Bochner- Hartogs theorem is proved for the case of hyperfunctions.
scientific article; zbMATH DE number 652220