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 ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Pseudo-Differential Operators and Applications Springer Journals

Inverse closedness and localization in extended Gevrey regularity

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Analysis; Operator Theory; Partial Differential Equations; Functional Analysis; Applications of Mathematics; Algebra
ISSN
1662-9981
eISSN
1662-999X
D.O.I.
10.1007/s11868-017-0205-0
Publisher site
See Article on Publisher Site

Abstract

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

Journal of Pseudo-Differential Operators and ApplicationsSpringer Journals

Published: Apr 13, 2017

References

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