# 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…

## One Citation

### An extension of the concept of exponential dichotomy in Fréchet spaces which is stable under perturbation

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In this paper we prove versions, in Frechet spaces, of the classical theorems related to exponential dichotomy for a sequence of continuous linear operators on Banach spaces. To be more specific,…

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