Inverse closedness and localization in extended Gevrey regularity

Inverse closedness and localization in extended Gevrey regularity We consider classes $$ \mathcal {E}_{\tau ,\sigma }(U)$$ E τ , σ ( U ) of ultradifferentiable functions which are extension of Gevrey classes, and prove that such classes are inverse closed. This result is used to construct an element from $$ \mathcal {E}_{\tau ,\sigma }(U)$$ E τ , σ ( U ) which is not a Gevrey regular function. Furthermore, we show that the singular support of a distribution $$u\in \mathcal {D}'(U)$$ u ∈ D ′ ( U ) related to local regularity in $$ \mathcal {E}_{\tau ,\sigma }(U)$$ E τ , σ ( U ) coincides with the standard projection of the corresponding wave front set $$ {\text {WF}}_{\tau ,\sigma }(u)$$ WF τ , σ ( u ) . Journal of Pseudo-Differential Operators and Applications Springer Journals

Inverse closedness and localization in extended Gevrey regularity

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Springer International Publishing
Copyright © 2017 by Springer International Publishing
Mathematics; Analysis; Operator Theory; Partial Differential Equations; Functional Analysis; Applications of Mathematics; Algebra
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