Beyond Gevrey regularity: superposition and propagation of singularities. (English) Zbl 1499.46078
Summary: 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.
MSC:
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
| 46E10 | Topological linear spaces of continuous, differentiable or analytic functions |
| 35A18 | Wave front sets in context of PDEs |
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