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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>.<ref>{{harvnb|Schapira|1985|loc=Ch. I., § 1.2.}}</ref> A section of that sheaf over an open subset <math>U \subset T^* X</math> is a formal series: for some integer ''m'',
:<math>P = \sum_{-\infty < j \le m} p_j</math>
where each <math>p_j</math> is a [[holomorphic function]] on <math>U</math> that is [[homogeneous function|homogeneous]] of degree <math>j</math> in the second variable.
The sheaf <math>\mathcal{E}</math> of microdifferential operators on <math>T^* X</math> is then the subsheaf of <math>\widehat{\mathcal{E}}</math> consisting of those secctions satisfying the growh condition on the negative terms; namely, for each compact subset <math>K \subset U</math>, there exists an <math>\epsilon > 0</math> such that
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