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^t _{r,d}, and by choosing m and g in other ways we obtain asymptotic expansions for (generalized) SG classes.
Asymptotic expansions for Hörmander symbol classes in the calculus of pseudo-differential operators.
CORIASCO, Sandro;
2014-01-01
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^t _{r,d}, and by choosing m and g in other ways we obtain asymptotic expansions for (generalized) SG classes.
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