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arXiv · 1411.3206

A Non-analytic Superposition Result on Gevrey-modulation Spaces

Maximilian Reich
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Abstract

After defining classical weighted modulation spaces we show some basic properties. In this work we additionally choose an approach in terms of the frequency-uniform decomposition and a discussion on the weights of modulation spaces leads to a definition of Gevrey-modulation spaces, where we leave the Sobolev frame and proceed to the Gevrey frame in order to get better results. We prove that Gevrey-modulation spaces are algebras under multiplication. Moreover, we obtain a non-analytic superposition result which gives rise to discuss the possibility to apply Gevrey-modulation spaces to non-linear partial differential equations.

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Maximilian Reich. 2014-11-12. A Non-analytic Superposition Result on Gevrey-modulation Spaces. https://arxiv.org/abs/1411.3206

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