Abstract
We consider semilinear equations p(x, D)u = F [u], where the linear parts p(x, D) are pseudo-differential operators of Shubin type, with symbols satisfying a global ellipticity condition in ℝ n . For classical solutions u ∈ H s (ℝ n ), s > n/2, we obtain properties of super-exponential decay and holomorphic extension, expressed in terms of Gelfand–Shilov classes.
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