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arXiv · 2402.10006

Globally solvable time-periodic evolution equations in Gelfand-Shilov classes

Fernando de Ávila Silva·Marco Cappiello
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Abstract

In this paper we consider a class of evolution operators with coefficients depending on time and space variables $(t,x) \in \mathbb{T} \times \mathbb{R}^n$, where $\mathbb{T}$ is the one-dimensional torus and prove necessary and sufficient conditions for their global solvability in (time-periodic) Gelfand-Shilov spaces. The argument of the proof is based on a characterization of these spaces in terms of the eigenfunction expansions given by a fixed self-adjoint, globally elliptic differential operator on $\mathbb{R}^n$.

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Fernando de Ávila Silva, Marco Cappiello. 2024-02-15. Globally solvable time-periodic evolution equations in Gelfand-Shilov classes. https://arxiv.org/abs/2402.10006

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