• Corpus ID: 119129876

On the generation of groups of bounded linear operators on Fr\'{e}chet spaces

@article{Costa2017OnTG,
  title={On the generation of groups of bounded linear operators on Fr\'\{e\}chet spaces},
  author={'Eder R'itis Aragao Costa and Alexxandro Silva},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}
In this paper we present a general method for generation of uniformly continuous groups on abstract Frechet spaces (without appealing to spectral theory) and apply it to a such space of distributions, namely ${\mathscr F}L^{2}_{loc}(\mathbb{R}^{n})$, so that the linear evolution problem \begin{equation*} \left\{\begin{array}{l} u_{t} = a(D)u, t \in \mathbb{R} \\ u(0) = u_0 \end{array} \right. \end{equation*}always has a unique solution in such a space, for every pseudodifferential operator $a(D… 
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