Strong Regularity and Microsupport Estimates for Multi-Microlocalizations of Subanalytic Sheaves
Complex Variables
2026-03-12 v1 Analysis of PDEs
Abstract
We introduce the notion of strong regularity for subanalytic sheaves and establish estimates for the supports and microsupports of their multi-microlocalizations. As applications, we study subanalytic sheaves of Whit- ney and temperate holomorphic solutions of regular D-modules along an involutive subbundle. In this setting we prove initial value theorems for multi-microlocal objects with growth conditions and division theorems for temperate and Whitney multi-microfunctions. As a consequence, we obtain a multi-microlocal version of Bochner's tube theorem for solution sheaves of strongly asymptotically developable functions.
Keywords
Cite
@article{arxiv.2603.10820,
title = {Strong Regularity and Microsupport Estimates for Multi-Microlocalizations of Subanalytic Sheaves},
author = {Ryosuke Sakamoto},
journal= {arXiv preprint arXiv:2603.10820},
year = {2026}
}