Microdifferential operator: Difference between revisions

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In mathematics, a '''microdiiferentialmicrodifferential operator''' is a linear operator on a cotangent bundle (phase space) that generalizes a [[differential operator]] and appears in the framework of [[microlocal analysis]] as well as in the Kyoto school of [[algebraic analysis]].

The notion was originally introduced by L. Boutet de Monvel and P. Krée<ref>{{harvnb|L. Boutet De Monvel, Louis|P. Krée}}</ref> as well as by M. Sato, T. Kawai and M. Kashiwara.<ref>{{harvnb|M. Sato|T. Kawai|M. Kashiwara}}</ref> There is also an approach due to J. Sjöstrand.<ref>{{harvnb| Sjöstrand}}</ref>

== Definition ==

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== See also ==

*[[pseudodifferentialPseudodifferential operator]]

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===Works===

* Aoki, T., Calcul exponentiel des opérateurs microdifférentiels d'ordre infini, I, Ann. Inst. Fourier, Grenoble, 33–4 (1983), 227–250.

* Boutet De Monvel, Louis ; Krée, Paul, Pseudo-differential operators and Gevrey classes, Annales de l'Institut Fourier, Volume 17 (1967) no. 1, pp. 295-323

* M. Sato, T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, in: Lecture Notes in Math. 287, Springer, 1973, 265–529.

*{{cite book |last1=Schapira |first1=Pierre |title=Microdifferential Systems in the Complex Domain |series=Grundlehren der mathematischen Wissenschaften |date=1985 |volume=269 |publisher=Springer |doi=10.1007/978-3-642-61665-5 |isbn=978-3-642-64904-2 |url=https://link.springer.com/book/10.1007/978-3-642-61665-5}}

* Sjöstrand, Johannes. Singularités analytiques microlocales, dans Singularités analytiques microlocales - équation de Schrödinger et propagation des singularités..., Astérisque, no. 95 (1982), pp. iii-166. https://www.numdam.org/item/AST_1982__95__R3_0/

== Further reading ==

* https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1723-09.pdf in Japanese

[[Category:Differential operators]]