Abstract
We establish formulas for asymptotic expansions for \(S(m,g)\), the Hörmander class parameterized by the metric \(g\) and weight function \(m\), defined on the phase space. By choosing \(m\) and \(g\) in appropriate ways, we cover some classical results on expansions for symbol classes of the form \(S^\tau _{\rho ,\delta }\), and by choosing \(m\) and \(g\) in other ways we obtain asymptotic expansions for (generalized) \(\mathrm{SG }\) classes.
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Coriasco, S., Toft, J. Asymptotic expansions for Hörmander symbol classes in the calculus of pseudo-differential operators. J. Pseudo-Differ. Oper. Appl. 5, 27–41 (2014). https://doi.org/10.1007/s11868-013-0086-9
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DOI: https://doi.org/10.1007/s11868-013-0086-9