On the Dimension Formula for the Hyperfunction Solutions of Some Holonomic D-modules

Abstract

In this short note we improve a recent dimension formula of Takeuchi for the dimension of the hyperfunction solutions of some holonomic D-modules. Besides the constructibility result and the local index formula of Kashiwara for the holomorphic solution complex, we only use a vanishing theorem of Lebeau together with a simple calculation in terms of constructible functions.