no. 3
Multi-microlocalization and microsupport
[Multi-microlocalisation et microsupport]
Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 3, pp. 569-611

The purpose of this paper is to establish the foundations of multi-microlocalization, in particular, to give the fiber formula for the multi-microlocalization functor and estimate of microsupport of a multi-microlocalized object. We also give some applications of these results.

Le but de cet article est d'établir les fondements de la multi-microlocalisation, en particulier, de donner une formule de fibre pour le foncteur de multi-microlocalisation et aussi une estimation du microsupport d'un objet multi-microlocalisé. Nous donnons également quelques applications de ces résultats.

Publié le :
DOI : 10.24033/bsmf.2723
Classification : 35A27, 23C38, 32C35
Keywords: Microlocal analysis, multi-microlocalization, microsupport.
Mots-clés : Analyse microlocale, multi-microlocalisation, microsupport. 
@article{BSMF_2016__144_3_569_0,
     author = {Honda, Naofumi and Prelli, Luca and Yamazaki, Susumu},
     title = {Multi-microlocalization and microsupport},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {569--611},
     year = {2016},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {144},
     number = {3},
     doi = {10.24033/bsmf.2723},
     mrnumber = {3558433},
     zbl = {1370.35023},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2723/}
}
TY  - JOUR
AU  - Honda, Naofumi
AU  - Prelli, Luca
AU  - Yamazaki, Susumu
TI  - Multi-microlocalization and microsupport
JO  - Bulletin de la Société Mathématique de France
PY  - 2016
SP  - 569
EP  - 611
VL  - 144
IS  - 3
PB  - Société mathématique de France
UR  - https://www.numdam.org/articles/10.24033/bsmf.2723/
DO  - 10.24033/bsmf.2723
LA  - en
ID  - BSMF_2016__144_3_569_0
ER  - 
%0 Journal Article
%A Honda, Naofumi
%A Prelli, Luca
%A Yamazaki, Susumu
%T Multi-microlocalization and microsupport
%J Bulletin de la Société Mathématique de France
%D 2016
%P 569-611
%V 144
%N 3
%I Société mathématique de France
%U https://www.numdam.org/articles/10.24033/bsmf.2723/
%R 10.24033/bsmf.2723
%G en
%F BSMF_2016__144_3_569_0
Honda, Naofumi; Prelli, Luca; Yamazaki, Susumu. Multi-microlocalization and microsupport. Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 3, pp. 569-611. doi: 10.24033/bsmf.2723

Delort, Jean-Marc Microlocalisation simultanée et problème de Cauchy ramifié, Compositio Math., Volume 100 (1996), pp. 171-204 (ISSN: 0010-437X) | Numdam | MR | Zbl

Fernandes, T. M.; Kashiwara, Masaki; Schapira, Pierre Micro-support and Cauchy problem for temperate solutions of regular 𝒟-modules, Port. Math. (N.S.), Volume 58 (2001), pp. 485-504 (ISSN: 0032-5155) | MR | Zbl

Honda, Naofumi; Prelli, Luca Multi-specialization and multi-asymptotic expansions, Adv. Math., Volume 232 (2013), pp. 432-498 (ISSN: 0001-8708) | MR | Zbl | DOI

Kashiwara, Masaki; Schapira, Pierre Sheaves on manifolds, Grundl. math. Wiss., 292, Springer, Berlin, 1990, 512 pages (ISBN: 3-540-51861-4) | MR | Zbl | DOI

Kashiwara, Masaki; Schapira, Pierre Ind-sheaves, Astérisque, Volume 271 (2001) (ISSN: 0303-1179) | MR | Zbl | Numdam

Koshimizu, Hiroshi; Takeuchi, Kiyoshi On the solvability of operators with multiple characteristics, Comm. Partial Differential Equations, Volume 26 (2001), pp. 1691-1720 (ISSN: 0360-5302) | MR | Zbl | DOI

Prelli, Luca Sheaves on subanalytic sites, Rend. Semin. Mat. Univ. Padova, Volume 120 (2008), pp. 167-216 (ISBN: 978-88-7784-301-2, ISSN: 0041-8994) | MR | Zbl | Numdam | DOI

Prelli, Luca Conic sheaves on subanalytic sites and Laplace transform, Rend. Semin. Mat. Univ. Padova, Volume 125 (2011), pp. 173-206 (ISBN: 978-88-7784-329-6, ISSN: 0041-8994) | MR | Zbl | Numdam | DOI

Sato, Mikio; Kawai, Takahiro; Kashiwara, Masaki, Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau) (Lecture Notes in Math.), Volume 287, Springer, Berlin, 1973, pp. 265-529 | MR | Zbl

Schapira, Pierre; Takeuchi, Kiyoshi Déformation binormale et bispécialisation, C. R. Acad. Sci. Paris Sér. I Math., Volume 319 (1994), pp. 707-712 (ISSN: 0764-4442) | MR | Zbl

Takeuchi, Kiyoshi Binormal deformation and bimicrolocalization, Publ. Res. Inst. Math. Sci., Volume 32 (1996), pp. 277-322 (ISSN: 0034-5318) | MR | Zbl | DOI

Uchida, Motoo A generalization of Bochner's tube theorem in elliptic boundary value problems, Publ. Res. Inst. Math. Sci., Volume 31 (1995), pp. 1065-1077 (ISSN: 0034-5318) | MR | Zbl | DOI

Yamazaki, S. Microsupport of Whitney function solutions to systems with regular singularities and its applications (2003) (preprint UTMS 2003-7, http://kyokan.ms.u-tokyo.ac.jp/users/preprint/pdf/2003-7.pdf )

Cité par Sources :