We extend the notion of specialization functor to the case of several closed submanifolds satisfying some suitable conditions. Applying this functor to the sheaf of Whitney holomorphic functions we construct different kinds of sheaves of multi-asymptotically developable functions, whose definitions are natural extensions of the definition of strongly asymptotically developable functions introduced by Majima.
"Multi-specialization and multi-asymptotic expansions." Proc. Japan Acad. Ser. A Math. Sci. 87 (5) 69 - 72, May 2011. https://doi.org/10.3792/pjaa.87.69