Microdifferential operator: Difference between revisions

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== Definition ==

We first define the sheaf <math>\widehat{\mathcal{E}}</math> of formal microdifferential operators on the cotangent bundle <math>T^* X</math> of an open subset <math>X \subset \mathbb{C}^n</math>. A section of that sheaf over an open subset <math>U \subset T~* X</math> is a formal series:

:<math>P = \sum_{\infty < j \le m p_j</math>

where <math>p_j</math> is a holomorphic function on <math>U</math> that is homogeneous of degree $j$ in the second variable.

== Reference ==

*{{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}}