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On some generalizations of Gevrey classes

✍ Scribed by Daniela Calvo; María del Carmen Gómez-Collado

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
193 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

We present a generalization of Gevrey classes, aiming at including the inhomogeneous Gevrey functions introduced by Liess [15] and the ultradifferentiable functions in the sense of Braun et al. [4]. Therefore, we treat the related dual spaces, called generalized Gevrey ultradistributions, proving also a version of the Paley-Wiener-Schwartz Theorem in our framework. Two different topologies are treated, following the lines both of Beurling [1] and of Roumieu [21], [22]. We finally treat in these spaces the well-posedness of the Cauchy problem for weakly hyperbolic operators, extending the previous results of Larsson [14] and Calvo [6], [7].

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