| Summary: | We study pseudodifferential operators with amplitudes $a_varepsilon (x,xi)$ depending on a singular parameter $varepsilon o 0$ with asymptotic properties measured by different scales. We prove, taking into account the asymptotic behavior for $varepsilon o 0$, refined versions of estimates for classical pseudodifferential operators. We apply these estimates to nets of regularizations of exotic operators as well as operators with amplitudes of low regularity, providing a unified method for treating both classes. Further, we develop a full symbolic calculus for pseudodifferential operators acting on algebras of Colombeau generalized functions. As an application, we formulate a sufficient condition of hypoellipticity in this setting, which leads to regularity results for generalized pseudodifferential equations.
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