= Formal pseudodifferential operator
{title2=$P=\sum_{j\leq N}p_j(x)\partial^j$}
A <formal pseudodifferential operator> is a series in <integer> powers of $\partial=d/dx$, bounded above but possibly infinite towards negative powers. Its <coefficients> are <smooth functions>. Multiplication uses the <formal pseudodifferential composition rule>. Negative powers are formal inverses, not globally defined integration operators on all <smooth functions>. Every <coefficient> in a product is a finite sum, so multiplication is defined without analytic convergence.
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