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Time-periodic Gelfand-Shilov spaces and global hypoellipticity on $\mathbb{T} \times \mathbb{R}^n$
- Publication Year :
- 2021
-
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 $\mathbb{T} \times \mathbb{R}^n$.<br />Comment: 32 pages
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2108.04368
- Document Type :
- Working Paper