# 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

, Volume 8 (3) – Apr 13, 2017
11 pages

/lp/springer_journal/inverse-closedness-and-localization-in-extended-gevrey-regularity-7rGYIeg8XE
Publisher
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

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