Interpolating Varieties and the Fabry–Ehrenpreis–Kawai Gap Theorem
✍ Scribed by C.A. Berenstein; T. Kawai; D.C. Struppa
- Book ID
- 102965643
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 936 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
dedicated to the memory of the late mr. y. taniguchi
1. Introduction
Ehrenpreis suggested that one could understand the Fabry gap theorem for functions of one complex variable from the view point of convolution operators. This idea was first carried through by Kawai [18], incorporating techniques from hyperfunction theory. This result has been extended further by Kawai [19] and Berenstein and Struppa [4, in several respects, but delicate issues inherent to higher dimensional problems remain to be solved. In this article we show how interpolation problems solved in Berenstein and Taylor [9, 10] can be effectively applied to prove a Fabry-type gap theorem in R n (n 2). These results have been announced in .
The method we use here is inspired by the study of R-holonomic complexes . In fact, the infinite order operators which we will use in Section 4 for our main results were first constructed by Kashiwara and Kawai [15] in the one-dimensional case as a realization of some abstract properties of R-holonomic complexes.