Division and extension in the Carleman class of holomorphic functions. (Division et extension dans des classes de Carleman de fonctions holomorphes.) (French) Zbl 0942.32011
Jakubczyk, Bronisław (ed.) et al., Singularities symposium - Łojasiewicz 70. Papers presented at the symposium on singularities on the occasion of the 70th birthday of Stanisław Łojasiewicz, Cracow, Poland, September 25-29, 1996 and the seminar on singularities and geometry, Warsaw, Poland, September 30-October 4, 1996. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 44, 233-246 (1998).
Let \(\Omega\) be a bounded pseudoconvex domain in \(\mathbb{C}^N\) with \(C^1\) boundary and let \(X\) be a complete intersection submanifold of \(\Omega\).
The author provides sufficient conditions for a given holomorphic function \(f\) in \(X\) to be extended to a holomorphic function in \(\Omega\) and to belong to a given strongly non-quasi analytic Carleman class in \(\overline\Omega\).
Also in this spirit, a version of division theorem for \(f\) is established. Discussions regarding those sufficient conditions are given.
For the entire collection see [Zbl 0906.00013].
The author provides sufficient conditions for a given holomorphic function \(f\) in \(X\) to be extended to a holomorphic function in \(\Omega\) and to belong to a given strongly non-quasi analytic Carleman class in \(\overline\Omega\).
Also in this spirit, a version of division theorem for \(f\) is established. Discussions regarding those sufficient conditions are given.
For the entire collection see [Zbl 0906.00013].
Reviewer: Vo Van Tan (Boston)
MSC:
| 32D15 | Continuation of analytic objects in several complex variables |
| 32E35 | Global boundary behavior of holomorphic functions of several complex variables |
