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arXiv · 2108.04368

Time-periodic Gelfand-Shilov spaces and global hypoellipticity on $\mathbb{T} \times \mathbb{R}^n$

Fernando de Ávila Silva·Marco Cappiello
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Abstract

We introduce a class of time-periodic Gelfand-Shilov spaces of functions on $\mathbb{T} \times \mathbb{R}^n$, where $\mathbb{T} \sim \mathbb{R} /2\pi \mathbb{Z}$ is the one-dimensional torus. We develop a Fourier analysis inspired by the characterization of the Gelfand-Shilov spaces in terms of the eigenfunction expansions given by a fixed normal, globally elliptic differential operator on $\mathbb{R}^n$. In this setting, as an application, we characterize the global hypoellipticity for a class of linear differential evolution operators on $\mathbb{T} \times \mathbb{R}^n$.

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Fernando de Ávila Silva, Marco Cappiello. 2021-08-09. Time-periodic Gelfand-Shilov spaces and global hypoellipticity on $\mathbb{T} \times \mathbb{R}^n$. https://arxiv.org/abs/2108.04368

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