Generalization of multi-specializations and multi-asymptotics (Algebraic analytic methods in complex partial differential equations)

The purpose of this paper is to report on a new description of geometry appearing in the multi-specialization along a general family of submanifolds and to extend the multispecialization. The notion of multi-asymptotic expansions is also extended. Locally we can construct new sheaves of multi-asymptotically developable functions closely related with asymptotics along a subvariety with a simple singularity such as a cusp