Inhomogeneous Gevrey classes and ultradistributions |
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Authors: | Daniela Calvo Luigi Rodino |
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Institution: | Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy |
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Abstract: | The inhomogeneous Gevrey classes, defined in terms of Fourier transform, are a natural extension of the standard Gevrey classes. We find equivalent characterizations and discuss algebraic and topological properties. We therefore introduce the dual spaces, the inhomogeneous ultradistributions, giving some equivalent definitions and corresponding algebraic and topological properties; in particular, a version of the Paley-Wiener-Schwartz theorem is proved in our framework. Finally, as an important example, the multianisotropic Gevrey classes and ultradistributions are considered. |
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