Multi-specialization and multi-asymptotic expansions

TL;DR

This paper extends the specialization functor to multiple submanifolds and constructs new sheaves of multi-asymptotically developable functions, generalizing previous concepts in asymptotic analysis.

Contribution

It introduces a multi-specialization framework and constructs new sheaves of functions with multi-asymptotic properties, expanding the theory of asymptotic expansions.

Findings

Defined multi-specialization functor for several submanifolds

Constructed sheaves of multi-asymptotically developable functions

Extended Majima's strongly asymptotically developable functions

Abstract

In this paper 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.