We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.
For an analytic functional $S$ on $ℂ^n$, we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in $ℂ^n$. We determine the directions in which every solution can be continued analytically, by using the characteristic set.
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