Beyond gevrey regularity: Superposition and propagation of singularities
We propose the relaxation of Gevrey regularity condition by using sequences which depend on two parameters, and define spaces of ultradifferentiable functions which contain Gevrey classes. It is shown that such a space is closed under superposition, and therefore inverse closed as well. Furthermore,...
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Veröffentlicht in: | Filomat 2018, Vol.32 (8), p.2763-2782 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | We propose the relaxation of Gevrey regularity condition by using sequences
which depend on two parameters, and define spaces of ultradifferentiable
functions which contain Gevrey classes. It is shown that such a space is
closed under superposition, and therefore inverse closed as well.
Furthermore, we study partial differential operators whose coefficients are
less regular then Gevrey-type ultradifferentiable functions. To that aim we
introduce appropriate wave front sets and prove a theorem on propagation of
singularities. This extends related known results in the sense that
assumptions on the regularity of the coefficients are weakened. |
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ISSN: | 0354-5180 2406-0933 |
DOI: | 10.2298/FIL1808763P |