Strong Regularity and Microsupport Estimates for Multi-Microlocalizations of Subanalytic Sheaves
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915854120124416 |
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| author | Sakamoto, Ryosuke |
| author_facet | Sakamoto, Ryosuke |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong Regularity and Microsupport Estimates for Multi-Microlocalizations of Subanalytic Sheaves Sakamoto, Ryosuke Complex Variables Analysis of PDEs 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. |
| title | Strong Regularity and Microsupport Estimates for Multi-Microlocalizations of Subanalytic Sheaves |
| topic | Complex Variables Analysis of PDEs |
| url | https://arxiv.org/abs/2603.10820 |